I was wondering if Steam or any servers will ban or auto ban users for inappropiate account names.

Are you referring to account names or nicknames? You can put anything as a nickname, unless some servers wants to ban you because of their reasoning. I don't really think inappropriate account names even matters, especially when even swear words are already "not available" when clicking the "Check availability" adds random numbers after it.

Anyways, why?

I know that many servers (at least on TF2) will kick/ban people if they use offensive names on their servers, but I really doubt account names matters.

Ah, I forgot about the nicknames 'cause I'm not very experienced with Steam. Since account names probably don't matter, what about inappropriate nicknames then?

It doesn't really matter though, unless some servers wants to rid of inappropriate names. There are people who have completely inappropriate sprays (Nudity, for example) and uses them anyways and doesn't get banned/kicked unless people know they are griefing others.

Ok thanks for the feedback guys.