You are “supposing” that it is. First, it isn’t.
Second, though, I’ll still answer the question.
My response would be to first ask “do you mean Pete and not Peter, or do you specifically mean Pete?” Then, if the answer comes back in the affirmative, I would ask “why?”
If the person had a good reason for using the nickname version, then I would write it that way in the official record.
I actually did have this happen once, not at a confirmation, but at a baptism (in principle the same for our topic here).
The parents wanted to baptize their son with a “nickname” version of a saints name. I’ll spare the entire narrative, but the reason was that this son was “the fourth.” His great-grandfather was baptised with that nickname version, and the oldest son of each generation was named likewise. While I was a bit surprised, it was not a problem, and I did not treat it as such.
You see, what we must remember here is that the Church forbids names that are contrary to the Christian faith. However, (contrary to popular belief) there is no requirement that names take any particular form–they don’t even have to be “saint’s names”. Catholics in the US have a long history of priests imposing their own choice of names upon parents, and for that reason, we priests need to be sensitive about not doing that in the present.
The other issue is to realize that our pronunciation of names evolve over the centuries (millennia even). When a perfectly Christian name comes into a new language, the native-speakers almost always eventually pronounce the name in a way that’s comfortable for them.
So, given that we have a 2000 year history of evolving name-pronunciations, who am I to tell an individual set of parents (or a confirmand) that they cannot do it?
What value am I protecting by preventing them?