Sure if you're actively working in that subfield. I took abstract algebra in university and remember we treated groups and commutative groups, but I can't tell

Sure if you're actively working in that subfield. I took abstract algebra in university and remember we treated groups and commutative groups, but I can't tell you what exactly rings were or what Abelian referred to. (But just like knowing the names of things is not the same as knowing things, forgetting these labels is not the same as forgetting the materials.) Naming things is important. Yes it just takes one googling, but in many cases you are interfacing with many different topics and just reading straight up the useful descriptive name would allow keeping the flow without having to look up stuff. Maybe this is more of a stumbling block for some than others. Often I find I have to make up mnemonics and other strategies like "the longer word is the one that ..." or "put the two terms in alphabetical order to match their descriptive names' alphabetical order". Again, this doesn't happen for terms we use every day. But if you use it every year or so, it's a stumbling block to have to ask "which one was that again?" when the descriptive name would immediately clear it up. I think it's mostly vanity and a "respecting the elders" and credit assignment thing that so many things are named for mathematicians instead of descriptive names. Having something named after you is like one of the biggest "awards" a mathematician can get. But this has no concern for didactics.