If the uncle honestly desires that, he will get an attorney who will guide him through the process. It takes an attorney, but can be done.
Your niece will call you her aunt or uncle.
uncle, niece
Your niece's children are your great nieces and great nephews, and you are their great uncle. Your uncle could be the father of your niece, and thus the grandfather of your niece's children.
No state in the US permits marriage between niece and uncle.
A niece's son calls his uncle his uncle, just like everyone else.The niece's son calls her uncle his great uncle. He is the great uncle's great nephew.
If you are a woman, you are great great aunt to your niece's granddaughter. If you are a man, you are great great uncle to your niece's granddaughter. In either case, your niece's granddaughter is your great great niece.
You are her great-aunt/uncle. She is your great-niece.
You are your uncle's niece. You and your uncle's children are first cousins to each other.
great niece
Your sister's daughter is your niece. If you are a woman, you are your niece's aunt; if you are a man, you are your niece's uncle. Your sister's son is your nephew.
'Niece' is what a little girl is to her uncle. 'Nephew' is what a little boy is to his uncle. The children also are the niece and the nephew of their aunt.
Uncle