Just learnt an anti-Gambit vs Queen's Gambit.

But i don't know the name of this defense gambit.  Please share if you know the name.

Here is a more sophisticated variation:

So basically trying the Jobava Londons attack but Queens Gambit?

The third and longest line.....There can be more variations. In general, the idea is that black should NOT play a6 to defend against white nb5 - nc7 attack. Instead Black will sacrifice its a-Rook for great positional advantage.

Not necessarily. If White doesn't attempt Nb5 attack, white is OK. But in that case White Bf4 doesn't pose any imminent threat, and it will be a desirable opening for black.

The gambit, I think, doesn't have a peculiar name but the opening is the Harrwitz Attack.

It's well-known that the most testing form of Bf4 Queen's gambit is after 1d4 d5 2c4 e6 3Nc3 Nf6

4Nf3 Be7 5Bf4

Black's is fine after 4Bf4 c5, and probably 4....d5xc4.

Right. So it looks like that 4.... c5 counter gambit is a good response against Harrwitz Attack.

That is the third variation i posted. The point is that white played Bf4 before Nf3 (which is called Harrwitz Attack, according to @Che_ssdave hereinabove). I always felt like that if white played 4.Bf4, black should play 4....a6 to stop white 5.Nb5 attack. What i learnt today is that white Nb5 attack can always be defended by counter-gambit 4...c5.

the bishop is worst on f4 in the queens gambit than it is on e3

that would become a different opening

be3 is actually worse than bf4, because it blocks your own e-pawn.

Computer says that bf4 is OK. A slightly better option is bg5 to pin the knight, but that is more defensive a move than offensive. So if white wants to play for win, it may choose bf4.

In top level chess Nc3, Nf3 and then 5Bf4 is more ambitious than the classic Bg5 because there are simplifying defenses like the Lasker, with Ne4, against Bg5.

Nc3 and 4Bf4 isn't very dangerous for black, even if white tries more solid tries than Nb5 which is outright refuted by Bb4ch.

QGD : Austrian Variation

No, not Be3, but rather, 4.Bg5! Another is 4.cxd5. And 3.Nc3, not 3.Bf4.

One other is 3.Nf3 Nf6 4.g3, leading to the Catalan.