You gotta learn to choose your battles and judging by your lost, he made fun of the name, not you. So what? Are you so attached to a name that you’d let yourself get that enraged over it?
I’m not asking that sarcastically or in a condescending way, just trying to get you to identify why something like that got you so upset so you can address that reaction and it’s source. To answer our question hell no, fighting and starting quarrels over everything isn’t alpha, hell it’s not even masculine in the first place.
I will say this, identify and defend your personal values but at least know why you cherish said values, why you think they’re worth defending, and how far you’d go to defend them, and enforce your own boundaries as well.