I mean there are sensible reasons for both people having the same surname - such as what to name the kids (if they have them). Incidentally I have noticed that my friends with hybrid/double barreled surnames tend to be those who don't plan to have children, but this could be confirmation bias/small sample.
On another note, I'd argue that to a certain extend the discrimination is towards the man in this regard. The bride can automatically change her name as part of the process of getting married, whereas the man has to go the formal route, outside of the wedding, the same as if anyone were changing their name.
I imagine the practical difficulty of the man taking the woman's name is an impact on which name they choose to keep as much as anything else.
I've no idea how name changing in a homosexual relationship works incidentally, does one of them get classified as the "bride" and get this automatic change?