Plus Wolverine's the only X-Man who wears a mask. They don't have secret identities. Jameson actually probably doesn't have a problem with them. He's...
Good point about the X-Men comics in Logan. And yeah, the deleted scene for Logan has Xavier talk about Wolverine being responsible for killing Jean...
Yes, perhaps someone with magic at that time in the past could detect her (Karnilla for example or whoever was before her) but she manages to prevent...