"Diminutive," I'd call it.
From The Cambridge Academic Content Dictionary (and similar definitions from other sources): Nickname-“an informal name for someone or sometimes something, used esp. to show affection, and often based on the person's name”I wouldn't say it was a nickname.
From a search engine: ”David Nicknames- Davy, Davey, Dave.”
This is not suggesting that Dave is a nickname, though. I'd think of a nickname based on Dave as something like Dave the Rave or Wavy Davy or Dangerous Dave or Davy Boy.
I'm not sure a search engine is a great authority on this.