what's the name of this opening


Yeah, depends on what you're doing as black. If you're playing d5 and g6 then those moves by white (and bishop to f4 or g5 and sometimes eventually to h6) can lead to big attacks. Otherwise the knight is usually slightly misplaced on c3 in d4 d5 openings.
Along with the Barry you might also google for the Veresov although I'm not really clear on the differences between these two and e.g. the Tarzan, Torre, and Trompowski attacks. They all sort of blend together in my mind
Black almost inevitably has to play the c5 pawn break though. You need play in the center or queenside to balance white's kingside stuff.