I think so, because that would only make sense

Probably, because who else lives with the name Black?

Well, Andromeda was a Black. But her last name became Tonks after she married Ted. So, I guess she is the only living person connected to the Blacks in some way I guess.

And perhaps if there is another Black, it think Grimauld Place no 12 belongs to him/her since it is Black's for generations

But Sirius left 12 grimmauld place to Harry

Yes he did.. that's why I think there is no Black left.. :)