Here's a page from a really useful book called Ohalei Shem published in 1912. It's basically a Who's Who of rabbis the world over, with their biographies and addresses (where applicable; in many locales, evidently, writing the name and town and province was sufficient. For example, if you wanted to write the Chofetz Chaim, you could turn to pp. 552 - 53 and see that it would be correct to address it to І. M. Каганѣ Радунѣ (Вилеи. губ.). It has a haskamah from R. Chaim Soloveitchik (and R. David Karliner and R. Chaim Ozer) in case anyone follows such things.
I don't know if anything quite like this existed before, but it surely was a useful book, and therefore many people would own it and many eyes would peruse its pages. So it's interesting to look at the advertisements. You can do that yourself (it's mostly rabbinic journals) but the one I'll mention is Romm's ad for the Chumash Torah Temimah. As an aside, there doesn't seem to be any real rhyme or reason for the length of the biographies, so I will permit myself to speculate that they are based on some combination of how interesting the life of the particular rabbi was and how acquainted the author was with him. Some examples of longer-than-usual entries are the one for Rav Kook ("Kouk"), R. Isser Zalman Melzer and R. Baruch Epstein.
There are entries for many notables and future notables. For example, there is one for the young rabbi who would be the Satmar Rav one day. The listings are basically all Orthodox, which is not surprising, although not all of the Eastern European variety. I did note that Dr. Lowy of the Bresslau Rabbinical Seminary seems to have slipped through, but I looked in vain for Solomon Schechter (but others, like Rabbi Z. P. Chajes are listed). Rabbi Moshe Dawid Kasuto of Florenz is listed too.
Here's the page for two rabbeim in RIETS (which I doubt was it called then). Note that they can be reached at the "Talmud-Seminar," which I guess was the author's imaginative name for the Yeshiva which would be Yeshiva University. Note also that the author can't make up his mind between "New Iork" and "Jork."
I'm afraid I've reached the end of the post, and I haven't mentioned the author/ compiler's name! It was Rabbi Shmuel Noach Gottlieb of Pinsk. Although I most certainly did not count, it seems to me that there are about 2000 separate entries (the index has 15 pages of 3 columns each, without 45 names per column).