Il tuo nome in the singular and il vostro nome in the plural are Italian equivalents of the English phrase "your name." Context makes clear whether a formal (case 2) or an informal (example 1) form of address suits. The respective pronunciations will be "eel TOO-no NO-mey" and "eel VO-stro NO-mey" in Italian.
"Name" in English means nome in Italian.
Paige is an English loan name in Italian.
Dylan is an English loan name in Italian.
Gary is an English loan name in Italian.
Assisi is an Italian loan name in English.
"Kelsey" in English is Kelsey, as an English loan name, in Italian.
"Hi! My name is..." in English is Ciao! Mi chiamo...! in Italian.
Desmond is an English/Irish loan name in Italian.
"Shaun" in English is the Italian name Giovanni ("John") or the Irish loan name Shaun in Italian.
"Hello! Your name is...?" in English is Ciao! Come ti chiami...? in Italian.
"Hello! My name is...!" in English means Ciao! Mi chiamo...! in Italian.
Regina as a last name in Italian means "queen" in English.