Dear Boy vs My Boy: The Wording of Canon
Fanon has Dumbledore say "my boy" just about every other line. But looking at canon, how often does he actually do it, and how does this compare to the similar "dear boy"?
Series count, across all characters:
"my boy": 3
"dear boy": 32
Dumbledore count:
"my boy": 0
"dear boy": 7
"my dear boy"/"dear boy":
A common term of endearment, Dumbledore and Slughorn do not at all have a monopoly on it: it is also used by Headless Nick, Dippet, Lockhart, Scrimgeour, Trelawney, and others. It's a flexible term: any time you want an adult character to indicate affection, consider using this.
"my boy":
This one is far rarer, used only Slughorn, Trelawney, and Wood, once each. Of those three, Wood is the only exclusive "my boy" user; Slughorn and Trelawney both use "dear boy" much more frequently.
Takeaway:
If you want your fic to sound similar to canon, stick "dear" in front of "boy" 10x more often than you don't. But still, use "dear boy" sparingly -- once every 33,880 words, to be precise.