no, Dan is.
Just the same: Danny comes from Daniel, so any nicknames would be Dan, Dani, Danny, Danielito.
dani is sometimes short for daniel
Dan is the third person plural form of the verb "Dar". It means "they give".
Dani Shushan's birth name is Daniel Shushan.
Dani Pedrosa's birth name is Daniel Pedrosa.
Dani Dorf's birth name is Daniel Dorf.
Dani Dotan's birth name is Daniel Dotan.
Dani Zuniga's birth name is Daniel Zuniga.
Daniel Lloyd Davey
Daniel Bizer goes by Dani.
Daniel Osvaldo goes by Dani.
Daniel Buira goes by Dani.