Yeah, Walkman is a name; we don't usually pluralize individual components of a name, we just add an s or an es, or sometimes (but not always) a trailing y becomes ies. But if we did plural by components it would be Walksman. :p (Personally, I try to pluralize compound nouns this way, cause I think it's fun. Even if it's not always appropriate or correct.)

I always saw it as an unmarked plural (like sheep/fish/etc). I also find it hard to not prefix it with Sony in my head. But I would definitely use Walkmen over Walkmans if pushed.

Personally, I don’t like non-standard plurals and take the opportunity of a new word not to carry the mistake through. I prefer “mouses” as well, for the plural of a computer mouse.

That’s what I’ve always heard, and said.