The Parent Agency by David Baddiel

Barry Bennett hates being called Barry. In fact it's number 2 on the list of things he blames his parents for, after number 1: being boring.
 
But there is a world where parents don't just have children. That's far too random. Instead, children are allowed to choose their parents. For Barry Bennett, this world seems like a dream come true. Only things turn out to be not quite that simple...