Not quite. The Barney in HL2 and its episodes is only ever called Barney. His last name is only mentioned in the end credits (where it does say Barney Calhoun), but in-game his last name is never once mentioned, by any character. I find that interesting, because literally every other NPC with more than two minutes of screen time has both a first and a last name, with the G-man being the only exception. Alyx is also called Ms. Vance, Eli is also called Dr. Vance, Kleiner has his first name Isaac (and his nickname Izzy), there's also Judith Mossman and Wallace Breen. Heck, even Odessa Cubbage has a full name.
Now, yes, there are NPCs with just a first or a last name. HL2 had Noriko, Winston and Leon at the rebel base where you get the buggy. Episode 2 had Sheckley and Griggs. But these are minor characters, with one appearance at most. Barney, on the other hand, is a major ally and character, but he's never given a last name.
In Blue Shift, the opening tram ride gives your character name as "B. Calhoun." Other characters only ever call you Calhoun, your first name is never once mentioned.
In materials outside the games themselves, the name Barney Calhoun is used a lot, and the developers have pretty much indicated that they consider the Blue Shift Barney Calhoun to be the canon Barney, who appears in HL2 onwards. This makes the separation in-game even more evident and jarring. It's as if Valve and Gearbox are covering their bases, just in case there's an ownership issue or something like that.
There are other elements in the HL1 expansions that show similar properties. Other characters such as Rosenberg from Blue Shift are never mentioned again. Adrian Shepard was put into stasis and then forgotten. Plot events such as Barney's escape, the nuke and Race X's invasion are never touched upon. Seriously, you'd think someone would mention the fact that Black Mesa was nuked, at the very least. But, at the same time, nothing is ever said to contradict those events. No one talks about Black Mesa still existing in an un-nuked state. No one ever says that Barney escaped alone from Black Mesa, without several scientists in tow.
The way I see it, Blue Shift and Opposing Force currently hover in some sort of quantum limbo between canon and fanfiction. Not confirmed by any of the games as canon, but not contradicted by anything either. For this reason, I also think we'll never see Adrian Shepard in any future Half-Life game, unless Gearbox makes it.