Because I think the question is worded poorly, let me give my example.
For me it’s the brand name. Not its reputation or history, but just how the name sounds. For example:
Omega - association with ancient greece, and also math and physics. 10/10 would explore space with one
Cartier - sounds french and expensive, is french and expensive; perfect for if I was rich and wanted to feel rich
Baltic - reminds me of the cold Baltic sea, perfect name for a dive watch; probably one of the reasons I love the Aquascaphe so much
Names that end with “ex” - generaly sounds like you’re lazily trying to look cool (Rolex is an exception, I don’t feel strongly about it)
So yeah I know it’s dumb but the brand name is the thing that is always plastered in big letters across the dial, I feel that the name should fit the style of the watch and also myself.
I’m very new to watches and also not american, so Hamilton just reminds me of Hamilton the musical lol