Of course: it's your surname. Unless, that is, unless you're a woman, married, who's taken on, as is custom, your spouse's surname as yours. Only your birth name would serve.
And, even then, were you a woman nowadays, it's not unthinkable that both your parents went against custom and your mother did not change to your father's name, but retained her own birth name, or, alternatively, like the Spanish, combined the two (though in English not with the word "and", but rather with a hyphen).
And -- chew on this -- what if your paternal grandmother got remarried after your grandfather had passed on? Or if she previously had been married and the further question arises which married surname was being sought?