Uh, well, I don't understand how you can want to know what a name means without knowing where it came from, but anyway, I went to ancestry.com's site. It lists Laramie as a variant of Laramee but with no meaning. So we know the original surname was Laramee. I then went to a French/English dictionary online and dicovered that ramee could possibly be the past participle of the verb ramer which means "to row" or "to work hard." So if this is true, then Laramie/Laramee could mean "the one who rows" or "the one who works hard."