Okay, so it's not normal.
It's me speaking, I say it's not normal here, so it's not normal. By your definition.
Of course if we dispense with the pendantry we would argue that the point of saying it's not normal is to highlight how it's inconsistent with the approach of society towards the rest of itself, so a society where women change their name to take their husband's is not normal because it's inconsistent with the rest of the mores regarding the interactions between men and women.
But that'd require not nitpicking a thing to pick a pedantic fight online that is a waste of time, so... not in the scope of this conversation, I suppose.