Simply, if you go to facebook.com/family you can search all Facebook profiles by surname. Not only that, but the search is created using an easy to remember web address, so you can share a search result page. For example, searching for the surname Zylberman would send you to the page:
which is the first page of search results for the surname Zylberman. Similarly, if you changed the 1 to a 3 at the end of the web address, you would be taken to the third page of results. Of course, these search result pages will change as new accounts are created, or old accounts are deleted, etc. so sending a result page might show the names you want to show someone in the short term, but may not show the same names later.
In addition to searching in English, you can search in other character sets, such as Hebrew:
There are actually more Zylbermans listed in Hebrew than in English, but that's likely because there are less alternate spellings in Hebrew. For the same name in Hebrew, it could be Zylberman, Zilberman, Zylbermann, Zilbermann, Sylberman, Silberman or Silbermann in English (only the variation Sylbermann does not show up on Facebook).
You can also browse surnames which is interesting. One thing you can see is how many surnames are fake on Facebook. Besides that you can see lots of variations of surnames you may not have thought to search. Like in searching, you can also browse in other character sets. When browsing, Hebrew started on page 14893 of the 'Other' character set listings when I tried to find it, which you can jump to by going to this page:
It may or may not be where Hebrew names start when you read this, but it's probably not too far off if you're reading this post not long after it was written. I could be mistaken, but it looks like Hebrew follows Armenian and is followed by maybe Farsi? When I searched, Hebrew names ended on page 17611, which means there are currently over 2700 pages of Hebrew names, or with 96 names shown per page, over a quarter of a million surnames in Hebrew on Facebook. I suppose its possible some of those names are actually in Yiddish and not Hebrew, but presumably the majority of them are Israeli users who have listed their names in Hebrew.
What if you want to search for names in Hebrew (or Yiddish) and don't know enough Hebrew to spell the name in Hebrew, or have a Hebrew keyboard to type it out? Try using Stephen Morse's Transliterating English to Hebrew in One Step web page, where you can type the name in English, and receive the text in Hebrew. There are slight differences in the transliteration in some cases if you choose onto the options: Sephardic, Ashkenazi or Yiddish. In the case of Zylberman, both Sephardic and Ashkenazi options return the same result (the same spelling I guessed above). Yiddish is less likely to be useful (and in this case no search results were found using the Yiddish tranliteration) for the simple reason that anyone who uses a Yiddish spelling for their name (as opposed to English or Hebrew) is not very likely to be on Facebook altogether. Once you get the text in Hebrew letters, you can copy that text and paste it into the Facebook search box.
So there you go, a super-easy way to search and browse surnames on Facebook, even using foreign alphabets.