I would use Patrick - like others have said, kids can make fun of everything, so unless it's something blatantly bad (if the initials spelled out PIG, for example), I would go with whatever you love.
Look at the popularity of the name Maddie right now - Fatty Maddie. Aiden is popular: Aiden and 'abettin (granted, this would be a taunt at an older age and not grade school).
Kids are cruel, but they are usually cruel at random, so there's nothing much the parent can do that will protect them from everything. And PP is a pretty tame insult and will hopefully be something that is outgrown quickly (if it even becomes an issue at all).