When is Research Assistant/Associate/Fellow a correct title for a PhD student?
How about "PhD student"?

Since you also asked about Germany: in German you can call yourself "Doktorand" or "Promovend". But also in Germany, "PhD student" would be perfectly fine.

If you want to leave out the "student" part, you might call yourself "PhD candidate".

Be careful to avoid calling yourself something you are not (e.g. "Dr."), since particularly in Germany that might be illegal.