Hi! It sounds like you have a wonderful pet rat! Such a happy cuddly guy! I've never had a rat before so I'm not sure what to name them, but I just had a choice between a female and male bunny and I got the female which is Kishii! If I got the male I was thinking of naming him either:

Eric or..

Yoru (It's japanese for evening)

I'm just obsessed with Eric from the Phantom of the Opera, that's why I chose that name lol. Just ignore me if they sound wierd haha. Yoru might be hard for a 2 yr old to say too.

Good luck with the name, I'm sure whatever you name it, it will love it's name!

I've Been Frosted