Is the alpha the only one to mark by biting or does the omega mark them too in the same way?
Guess what I'mma say? Depends on your AU and what you are trying to get across.
In mine, it's kind of old-fashioned and makes an Alpha look controlling for just them to mark their omega/partner. People would look at their relationship like the Alpha is not the best person. It's also thought that the Alpha doesn't have love for their partner either. Or they think that the Alpha is just trying to bond with anyone that they can while their bonded partners are left reeling.
All-in-all, in my AU, the Omega bites them in the same way. In fact, when an Alpha and Omega bite one another they have a crazy strong bond. If they are soul mates/perfect pairing, they will be able to have almost psychic abilities for one another. That's a post for another day though.