Noah-Lutz: Who's who?

Note: don't expect "realism" here. The ideas are really weird.

Well, I don't have a "theory" for this. What's more, I almost don't care about it. I remember that the first time I saw Lut'z pic in PS2 I said "This is Noah". Now I don't know. Here are a few possibilities:

1- The classic one: Lutz was Noah's sucessor.

2- Noah decided to change his name for "Lutz".

3- He suffers from Double-Personnality.

4- Lutz is his son or twin brother.

5- Noah cloned himself, named his "other-him" Lutz and escaped from the Mansion.