Before I outline the problem, let's lay out some assumptions and facts.
First, there is no doubt that the Hebrew אבן, sometimes written as ן'י, used as part of the name of many Spanish Jews and their descendants is the Arabic word ابن, son of. The usage is equivalent to the Hebrew בן, although it need not always refer to the person's father. It often refers to a grandfather or other ancestor, which is also an accepted, expanded use of בן. Furthermore, in Arabic the word is pronounced ibn, subject to an important qualification. The qualification is that it appears that the Spanish Arabs did not pronounce it ibn, but rather pronounced it aben (please note, incidentally, that the vowel shift here is the same as that between two of the possible pronunciation of the word רבי). The following entry is from E.J. Brill's first encyclopaedia of Islam, 1913-1936, Volume 1:
Thus, it would seem likely that Ibn Ezra (and all, or most other Sephardim) pronounced it aben and not ibn, as the current common practice is. My assumption is that the way which Ibn Ezra himself pronounced it should carry some weight, even if it differs from how we pronounce it.
Below is the entry אבן in Elijah Levita's Tishby (Blogger doesn't do nekkudot well):
That was from the 1541 Isny edition. Please note that the image is a composite. אבן is actually the second entry, and extends to two separate pages, with Latin translation in the middle. I'll admit that I am unsure why the entry is vocalized with a tsere, while all instances receive a segol in the entry itself. This does not seem to be a mistake, since the book includes a list of corrections by the author at the end and this is not mentioned. In addition, it should be noted that the author was a grammarian whose method is to vocalize according to grammatical principles rather than usage. This can be seen all over his works, where words are vocalized in ways in which we are not used to (mainly because he did not succeed in pressing those vocalizations into common use). In addition, he often criticizes conventional vocalizations for being grammatically impossible. For example, he roundly rejects the vocalization of רבי with a sheva under the resh and a dagesh in the beis as impossible. This vocalization was common in manuscripts, see below. He assigns, rather, a chirik under the resh as correct. His observation was seconded by Rabbi Jacob Emden two centuries later, however his solution was to retain the sheva, but change the beis to give up it's dagesh.
Below is a beautiful late 13th century manuscript (from the Kauffmann collection, ms 388a) which vocalizes רבי in exactly the way that Levita and Emden realized were (grammatically) impossible:
Here is how Rabbi Emden discusses the vocalization:
While I'll admit that for some reason it looks like the ב has a dagesh (and I can't explain it, unless it's a typographical error or the result of a bad scan), elsewhere Emden reveals more:
This is from his comment on the first Mishna of the second chapter of Avos. As you can see, he reiterates his contention that the resh receives a sheva, however he also comments on the proper vocalization of רבי as the title for Rabbi Yehuda Ha-nassi. In his opinion this word is different from conventional occurrences of the word, for it does not mean "rabbi" the same as the conventional title, but is more personal, meaning "My master [rabbi]." Thus, rather than point it with a sheva it receives a patach (ra-). More importantly, he spells out that the ב has a dagesh. I believe I am not incorrect in inferring that according to him in the conventional occurrence the ב does not have a dagesh. This would be the same grammatical error that R. Elijah Levita corrected. Indeed, in later printings of Rabbi Emden's siddur the ב has no dagesh, and there is a parenthetical insertion affirming this after R. Emden's original comment. Whether this is proper without clearly stipulating that it's an addition by a later editor is a perfectly fair question.
But we hardly need to make pilpulim like the one I just made. On page יט of his Luach Eresh (letter נ) he says it explicitly:
And here is how his predecessor Rabbi Solomon Hanau points it in his Siddur Beis Tefillah, a truly wild solution, although arguably not any more wild than what is, essentially, "Rivi", being that both are unprecedented:
To add another wrinkle, below is a comment in Johann Reuchlin's De Arte Cabbalistica (1517):
" . . . On this, David Kamchi -- Or Kimchi, in our pronunciation (like the way some say rabbi, and the Germans say ribbi because it's easier; and like the divergence of opinion of Greek and Latin on grammatiki and grammatica, and logiki and logica, mitir and mater, and so too Samson and Simson, Kamchi and Kimchi, and so on) -- anyway, this Jew, David, a Spaniard, teaches . . . "
Amazingly, he writes that the Germans say ribi. This seemingly contradicts the testimony of R. Elijah Levita, who lived at the same time. However, it's possible that i was Reuchlin's closest equivalent of how the Germans pronounced chataph qomatz, which is itself interesting. Of course one would like to know how Germans pronounced the Latin i in the early 16th century!
Since this post is ostensibly about ibn and not rabbi, getting back to Levita's entry for אבן we can also see his tendency to vocalize according to grammatical rules from the way he vocalized Tibbon and Gabirol. In both cases he conformed with Hebrew grammar and omitted the dagesh, although in Arabic (and these names are Arabic) they would receive a dagesh. I can't say much about his decision to vocalize what we call Tibbon as Ta[bb]on, because I am not certain if he did it for Hebrew grammatical or another reason. I will say that Tabbon seem to conform to the shift we see in Aben, which seems to be the Spanish Arabic pronunciation. My purpose in noting that his vocalizations would seem to be motivated more by grammatical correctness than by usage is to demonstrate that there needs to be some suspicion, or at least caution, on his value as a witness.
However, he is far from the only witness to the pronunciation of the Arabic ابن written in Hebrew as אבן as Aben. Essentially it is always written so in European languages until well into the 19th century.
Below are some samples:
Sebastian Muenster, 1527:
A very typical example from 1723:
In fact as near as I can tell "Ibn Ezra" simply does not make an appearance until the 1820s. It is surely possible that there are some stray examples before then -- I have found a couple of "abn"s:
But apart for that possibility, it seems certain that the 1820s was when "aben" began to give way to "ibn." Why "ibn" was never used before the 1820s, and became about equally used as "aben" in the rest of the 19th century, and to be almost totally preferred in the 20th is an interesting question. Tentatively one assumes it has to do with increased exposure to modern Arabs in the Levant. In fact, here is how it is written in the German edition of Jehoseph Schwarz's Das heilige Land (1832):
This in addition to many other citations of Arab names with "ibn." Old habits die hard, and look how Isaac Leeser writes it in two separate places in his 1850 translation of Schwarz, "The Holy Land":
What is clear is that "ibn" was on the ascent as being scientifically more correct, and "aben" on the way down. As the century progressed almost every mention of medieval Arab philosophers with "Ave-" names includes a note that it is a "corruption" for "Ibn" Whatever.
Although it isn't necessarily clear what conclusion to draw from the following, late samples, it seems possible that some Jews understood אבן, at least with respect to Ibn Ezra, as an abbreviation for אברהם בן. It would seem me then that they must have pronounced it Aben, and not Eben (or Even), and certainly not Ibn.
For example, in a work printed in1853 we find א"בן:
Here's אב"ן in a Yiddish work from 1894:
and there are many more such examples.
In any case, writing in 1896, here is Steinschneider:
As we can see, he is less certain that the author of the Encylopedia entry who asserts that it is how Spanish Arabs pronounced it. Still, this brings us back to Levita, who was close in time and place to Spanish Jews, and presumably he knew how they pronounced it. However it should be noted that he doesn't explicitly make this claim. Rather, the example he gives is the pronunciation of the names of Arab scholars, like Avicenna. However, we know this is how European scholars pronounced it. Do we (and he) know that this was how the Arabs, in Spain at least, pronounced it? Nevertheless, he must be given weight since, as I said, he was familiar with Spanish Jews. In fact, he was already an adult by the time of the expulsion of 1492.
Finally, writing in 1873 Michael Friedlander gives this note:
In conclusion, the upshot seems to be that "ibn" is an anachronism. Not necessarily wrong in the same sense that calling the subject of our post "Abraham" is wrong; that's merely a translation of his name into English. In all likelihood Aben or something close was how Spanish Jews with אבן or ן'י as part of their full name pronounced it. Thus "Aben Ezra" is fully justified.