Usually you have some kind of detection method using regex and a blacklist of words. This is quite a can of worms though if you do it yourself. If you have a server, you probably want to do this server-side, otherwise it could be circumvented. And it's not trivial to properly filter things out. Say you wanna filter the word "asshole". But what about "assh0le", "assho1e", "a$$hole". And if you filter "ass", what about "assemble" or "bass". Even big companies struggle with this actually, Minecraft being in most recent memory, e.g. the "diamond hoe". But big companies usually have some kind of reporting system with the option to report someone for "inappropriate username" like Overwatch for example. Because it's almost impossible to not have something slip though the cracks.
Hope that helps.