Can I do this with MusicBee?
On the surface, yes...
I'm just not too sure I understand correctly what you mean by "automatically put them in a correctly named folder".
Would you be referring to a folder structure in MusicBee only or on Windows Explorer as well?
If the latter, I'm guessing you are asking about whether or not it'd be possible to set some auto-organize (renaming) rule?
If so, that is quite possible too.
I already spend hours on end on social media. Might as well spare a few of those to a greater purpose here.