Do I need to mention my characters name?

The idea behind the current project I’m working on is a kind of jumbled up diary that’s been found detailing out of order adventures all written by the same person. There is no other points of view in this and I’d prefer it if there wasn’t any because every chapter begins with ‘dear diary,’ and the chapters themselves are all just written as regular diary entries.

My issue comes from the fact that you don’t usually use your name in a diary because it’s not necessarily addressed to anyone so they don’t need to know who you are. And since you wouldn’t usually expect people to read your diary why would you add anything to indicate who you are? Should I just sign off each entry with the characters name? Do I even need to name the character? Do I add some kind of dialogue that the character is recounting to kind of subtly name drop them?

Sorry if this is a dumb question I just haven’t planned this book at all and would prefer not to have to go back and mention their name a bunch of times and fit it into already existing chapters if I can help it (I’ve only written chapter 1 so far though)