Well, it's not hard to work out which of the two cities is viewed less positively, and I am born and bred from there!
Many tour companies and even some airlines already market the airport as just 'Leeds' rather than it's full name of Leeds/Bradford. I don't think a fancy name change is required, Leeds is a big enough city for overseas travellers to know where the airport is located. I wouldn't kick up too much of a fuss if Bradford was dropped from the name, most outside of Yorkshire seem oblivious to it being there in the first place! However, it will never happen so long as Bradford Council retain their slice of ownership.
Should the airport ever be sold off, then maybe.