I found this database.

Mongolian etymology

Since it's an etymology database, probably won't be able to get actual names/meanings that auto-translators will recognize, but maybe someone can get some use out of it.

Despite pages being numbered rather than lettered, it is still in alphabetical order, shouldn't be too hard to find a word that sounds like something you're looking for.

I used it to basically find a word close to my lalafell's name in middle or written mongolian and changed it a tiny bit. Sure, they're not really names, but I'm satisfied with what I got.