Would it be grammatically correct to also say Centrum Fabryka?
yes, it would be a center named Fabryka, nothing to do with with women though.
Softsong: Centrum Fabryka Yep. I like it.
If you like it, go for it, sounds good. Could be also the name of a place, like a club or some music center. It sounds a bit industrial and off the mainstream.
It seems that you like hard consonants, so here are a couple more verry bright ideas:
karuzela
zadra
Stradom (part of Kraków)
netoperek - one of the Polish jokes about the Czech language, this one is supposed to mean Batman in Czech, actually it's a modification of Polish "nietoperz" - bat. I think it sounds good.