Ella is Emma's mother.  Technically her first name is Lily and her middle name is Ella but for 'reasons' she goes by her middle name.  Whether Emma knows her mother's first name is actually Lily or not is debatable but it's likely she wouldn't have used that as the name for her false profile if she did.

In any case, because the package was simply addressed to 'Lily', Ella was able to claim it, and thus Noah, as hers.

And yeah, Stargate1990 specifically requested all the endings end with Noah lodged in a beautiful, plump backside lol