What is your name?/My name is...

American Sign Language:
"What's your name?" is signed in ASL as "your name what".
Your http://commtechlab.msu.edu/sites/aslweb/Y/W4552.htm
name http://commtechlab.msu.edu/sites/aslweb/N/W2442.htm
what http://commtechlab.msu.edu/sites/aslweb/W/W4456.htm

"My name is" is signed in ASL as "My name...then your name is fingerspelled".
My http://commtechlab.msu.edu/sites/aslweb/M/W2434.htm
name http://commtechlab.msu.edu/sites/aslweb/N/W2442.htm
...then fingerspell your name.

English:
What is your name?
My name is...

French:
Comment vous appelez-vous?
Je m'appelle...

Italian:
Come si chiama?
Mi chiamo...

Spanish:
¿Cómo se llama Usted? (formal)
¿Cómo te llamas? (informal)
Me llamo... (both formal and informal)

Swahili:
Jina lako nani?
Jina langu ni...

To learn to ask, "What is your name?" in over 330 languages, please visit this site: http://www.elite.net/~runner/jennifers/yourname.htm
To learn to say, "My name is..." in over 275 languages, please visit this site: http://www.elite.net/~runner/jennifers/myname.htm