I've only ever heard (seen, actually) the Peter = penis equation in an American context. Never in a British text, and certainly never here in South Africa, so I used it for my son without compunction. I also like Patrick, but I obviously prefer Peter.
In the 18th century, Patrick had a very negative Irish connotation in England and Patricks who wanted to make it in London society used to call themselves Peter, the better to blend in.