Indeed I can't find in Polish any other singular -anin not derived from place, But słowianin in plural is słowianie, and there's lots of -anie words not derived from places.
For example abstract nouns formed from verbs, like:
pisanie (writing) from pisać (to write)
palenie (smoking) from palić (to burn)
śniadanie (breakfast) from archaic śniadać (to eat)
jedzenie (food) from modern jeść (to eat)
bieganie (running) from biec (to run)
etc. There's easily hundreds of these.
Then it would be
słowianie (abstract noun for people who can talk) from archaic słowić (to express in words)
The only weird thing would be that słowianie is plural and all of the other -anie nouns made from verbs are singular.