Let’s ask Ibsen. Hey, Ibsen, why did you call it "Hedda Gabler" if the woman’s name is "Hedda Tesman?"
Ibsen, in his writing: "My intention in giving it this name was to indicate that Hedda as a personality is to be regarded rather as her father's daughter than her husband's wife."
So, Gabler is Hedda’s maiden name. She’s only been Hedda Tesman for six months by the time we join the action, and in case you couldn’t tell, names are pretty significant here. (Just check out "Symbols, Imagery, Allegory" for about eight other examples.) Now that we’ve got that nailed down, back to Ibsen’s comment: in what way is Hedda "her father’s daughter rather than her husband’s wife?"
For one, she has absolutely nothing in common with George. Actually…she kind of hates him. She misses her old life (her Gabler life) and her old identity (her Gabler identity). In fact, she seems to resent marriage (her Tesman marriage) altogether. Notice how she hates George’s slippers but is enamored with General Gabler’s pistols? Exactly.