I just generally call it "that Totoro one". In my defence, it allowed me to avoid the awful American spelling of neighbour. Also in my defence, let's face it, if we want to get technical about such things we could go and say Tonari no Totoro or となりのトトロ. Yay Wikipedia?

Will happily concede that My Friend Totoro is not the correct translation and settle on My Bro Totoro.