Resident of the UAE here. My child and I have different surnames, and once I have been questioned coming into the country with him (“where is your husband??”).
There was some talk in the UAE papers last year about new requirements for travel with minors, but seemingly nothing official ever got released and it appeared that it was possibly specific to travellers arriving from India.
Immigration are unlikely to bat an eyelid if all travellers have the same surname, based on what I have been told by friends who travel in and out frequently. That said, always better safe than sorry, in my opinion, and you never know if you’ll get an immigration guy in a bad mood.
I always travel with my child’s birth certificate and a letter of no objection from my husband. Have also been questioned in the UK, but that’s beside the point here.