yes, it has a subject and a predicate
Fer-ari
You should replace 'demo' with 'desu ga,' as 'demo' isn't used to connect two sentences, but is instead used to start new ones. Second, I have to point out that unless you're making it clear to others that you're joking, you should never refer to yourself as 'san.' 'San' is used to show respect to other people, and attaching it to your own name makes you seem quite arrogant and rude, or at least a good deal foolish. I think a better sentence would be, 'atashi wa katono ari desu ga, tomodachi wa ari to yobimasu.' "My name is Katono Ari, but my friends call me Ari."
Ari Boulogne goes by Ari.
Her nickname is Ari
Ari Telch's birth name is Ari Telch Benforado.
Ari Averbach's birth name is Ari Michael Averbach.
Ari Borovoy's birth name is Ari Borovoy Hofman.
Ari Behn's birth name is Ari Mikael Bjrshol.
Ari Fleischer's birth name is Lawrence Ari Fleischer.
Ari Piispa's birth name is Ari Tapio Piispa.
Ari Peltonen's birth name is Ari Pekka Peltonen.
Ari Zagaris's birth name is Ari Nicholas Zagaris.