move to my next door

 My friend is going to move into next door.

Or

 My friend is moving into next door.

You’d say this most likely if you are at your residence.

My friend is going to move next door to me.

Or

 My friend is moving next door to me.

You’d say this most likely if you are not at your residence

 My friend, Gongyou, is going to move next door. 

Adding the name does not change the correctness of this statement. Also, you should use a comma after your friends' name.

Hi guys,

I would most naturally say '. . . move in next door'.

Clive

lochel

You move into a house.

You move to a country.

 

My personal choice of statements are:

My friend is going to move into next door.

My friend is moving into next door.

No, I can't agree. You cannot apply "into a house" to "move into next door. (Just like you "go home" and not "go to home.") You do move into a house, but you move (in) next door.

But, for everyday use its just fine.