I’d definitely go with the second one. It’s not incredibly weird to call someone one name in one instance and another someplace else (for me at least.) He probably did it just because everyone else did and it made sense to not confuse people?
Yeah, it’s odder in comparison to other Gondorians than in itself. Faramir, for instance, persistently calls him ‘Mithrandir’ even to Frodo and Sam—and slips into Quenya names now and then (Laurelindórenan!). Same with Pippin (apart from the Quenya—though the hobbits don’t switch much to other people’s usages). But it’s not that hard to envision Boromir and Legolas as more adaptable, particularly as Sindarin-speakers in a mixed group in the North.