Well actually, regardless if Gnostics called themselves Christians, Christian doctrine itself evolved against the idea of Gnosticism. You can say “oh there’s several elements that appear to overlap with Gnostic ideas”, but essentially every single concept in Gnostic Christianity is completely spoken against by Christian doctrine. The concept of the distant creator god and the evil god of the Old Testament, the concept of Christ being a purely spiritual being, and every other major theme within Gnostic thought is completely condemned by the Church. Paul’s concepts of “putting off the flesh and putting on the Spirit” are actually not Gnostic, but are clearly saying “live in the way that god wants you to and not in the way you see fellow pagans behave”. Also, if by Gnostic elements in the Gospel of John you mean the Logos hymn, you would be very mistaken. The Logos hymn seeks to say Jesus is God and became human, which runs contrary to what the Gnostics were saying.

The only legitimate way Gnostics influenced Christianity was the counter against them in every way. To quote Gnostic concepts as if they were Christian is completely false.