When Henrik Ibsen finished writing Hedda Gabler in November of 1890, he sent the play to Count Maurycy (Maurice) Prozor, to have it translated into French prior to publication.

In December, 1890 Ibsen sent a letter to Count Prozor in which he wrote,

The title of the play is Hedda Gabler. 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 as her husband's wife. It was not my desire to deal in this play with so-called problems. What I principally wanted to do was to depict human beings, human emotions, and human destinies, upon a groundwork of certain of the social conditions and principles of the present day.

Hedda is the daughter of a General, now deceased, and prior to marrying George Tesman, an academic interested in historical studies, she enjoyed a privileged, aristocratic life, and moved freely in society.

At the beginning of Hedda Gabler, Hedda and George have returned from an extended wedding trip.

Now Hedda Tesman, and pregnant with George's child, in her own mind she's still Hedda Gabler, moving freely in the upper levels of society, and still in love with Eilert Løvborg, a former suitor who "made good" by publishing a book while Hedda has been away on her six-month honeymoon with George. One of the reasons Hedda married George was that she thought he would be famous, but Eilert has already passed him by.

Hedda and George have moved into a comfortable home, a former cabinet minster's villa—"spacious, handsome, and tastefully furnished," according to Ibsen's stage directions—but certainly smaller and less opulent than where she lived prior to her marriage.

Hedda's circle of friends has diminished considerably, and so has her self-identity. Once she was Hedda Gabler, daughter of the General, and a woman of the world. Now she's Mrs. Tesman, wife of a university researcher, living in the western side of Christiana (now Oslo). Quite simply, Hedda's world is changing. It's getting smaller, and it's closing in around her.

Ibsen describes Hedda on her first entrance into the play, and he presents her as retaining characteristics of her previous life as Hedda Gabler:

HEDDA enters from the left through the inner room. Her face and figure show refinement and distinction. Her complexion is pale and opaque. Her steel-grey eyes express a cold, unruffled repose.

Hedda makes small talk with George's aunt (Miss Tesman) and a local friend, Berta, and she gives some insight into the changes that have been happening in her life:

MISS TESMAN: Good morning, my dear Hedda! Good morning, and a hearty welcome!

HEDDA: Good morning, dear Miss Tesman! So early a call! That is kind of you.

MISS TESMAN: Well—has the bride slept well in her new home?

HEDDA: Oh yes, thanks. Passably.

GEORGE TESMAN. [Laughing.] Passably! Come, that's good, Hedda! You were sleeping like a stone when I got up.

HEDDA.: Fortunately. Of course one has always to accustom one's self to new surroundings, Miss Tesman—little by little.

Midway through the play, Hedda declares to Mr. Brack, "How mortally bored I’ve been."

Hedda tries to expand her world by manipulating and controlling the lives of the people around her, and by living vicariously through them. She steals a valuable document from George's dying aunt, goads Eilert into drinking again, burns the manuscript of of his second book, and urges him to commit suicide.

When Hedda is confronted by Mrs. Elvsted about her treatment of Eilert, Hedda replies, "For once in my life, I want to control a human destiny." Hedda can't even control her own life.

Ultimately, Hedda Gabler decides that she can't continue to live in the world of Hedda Tesman and commits suicide to release herself from her stifling, oppressive existence.

Ibsen’s use of the title “Hedda Gabler” is significant in that it says a great deal about how the protagonist sees herself, her class identity, and her relationship with Tesman. Hedda is the daughter of General Gabler who is an aristocrat. She has married down in class to the bourgeois George Tesman. She still thinks of herself primarily as an aristocrat and the daughter of the General rather than as a member of the bourgeois class, and assumes that she will continue to have rights to a life of luxury and deference from the lower classes as a matter of her birthright, rather than accepting her own situation as Tesman’s wife, which she finds stifling and uncomfortable.

Why is Ibsen's play titled Hedda Gabler instead of Hedda Tesman?

Henrik Ibsen's 1890 play Hedda Gabler was initially met with bad reviews and little public interest, but it has since become a classic drama and is compared favorably to Hamlet, among others.

The title of the play is odd at first. Although Gabler is Hedda's maiden name, she is married to Jørgen Tesman, and so her married name -- and that by which everyone knows her -- is Hedda Tesman. The choice to name the play after her original name and not her married name is explained by Ibsen here:

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.
(Ibsen, 1890 letter to Moritz Prozor, dlibrary.acu.edu.au)

There are, of course, other interpretations, but Ibsen's explanation is solid: Hedda is not a person entirely wedded to Tesman; in fact, her connection to him is less than her connection to her father, and in fact to herself. She is an individual, not an extension, and her actions are not those of a happily-married, ordinary person, but a very complex and possibly unstable individual who sees herself as a driving force in the lives of the people around her. She has a uniquely self-assured knowledge that she is entirely capable of affecting events without needing permission from the husband whose name she carries.

In fact, it can be said that she is a stronger character than all the others, as she acts for her own self-interest instead of tempering her desires; only the realization that she has accidentally given someone else leverage over her is enough to break her will.