Is this the Scandinavian Defense? Which side would be considered to have the advantage in this position?

Yes, that is one variation, a dangerous one though. The safe way is to play 4.d4 and transpose into a Caro-Kann.

I play 3.d4 and just give back the pawn, I'm usually able to get a good attack that way.

The position you cite can occur from a wide variety of openings, including the Scandinavian, Caro-Kann, Nimzo-Indian, Queen's Gambit Declined/Accepted, and the Sicilian, so the study of this can reap huge benefits.

As far as "advantages" go in this position, we have white with IQP (isolated queen pawn) and more space and black with target on d4 and solidity. Which side is better? The side who understands and implements correctly the appropriate plan!

A wiser, stronger player once advised me to learn how to play BOTH sides of such positions.

An excellent book which covers these topics is Alexander Baburin's "Winning Pawn Structures", which discusses ideas and plans from both sides of the board.