Chico
 

¿Es Chico también un nombre?

This implies that it is:

Yes, Chico is a name like Chuck, not like Charles. I think it doesn't come from other name like Quico comes from Federico or Pepe from Pedro. A good example is an old Argentine singer, Chico Novarro, whose real name is Bernardo Mitnik Lermann.

Oh ok, that's pretty cool. But does that mean that it sounds like you're addressing the other person as "Boy!"?

And is Chica also a name?

Chico Buarque de Holanda, su nombre verdadero es Francisco.
No sé si en Brasil a todos los Francisco los apodan Chico o es sólo referido a este artista por su cara y modos de "buen chico". Entonces sería un "mote".
Quico o Kiko lo conozco también para los Enrique y Pancho para los Francisco. A los José, Pepe y a los Pedro, Perucho.
Gullermo = Memo.
Patricio = Pato.
José Patricio, típico doble nombre que durante un periodo era muy común entre los "jaivones" (Highborns) chilenos, PepePato con su Volvo rojo. Me refiero a la mitad de los años '60, del siglo pasado.

I'm not sure as Chico is not common here. It sound like Caribbean Rim or at least tropical/subtropical to me. I don't think they are addressing a person as a "boy". At most "the youngest" or "the shortest", but I don't think this either.

I've never heard of a person named "Chica".

How about Nacho? I just saw this bilingual children's book in the store entitled "Uncle Nacho's Sombrero". I almost burst out laughing. Is that a real name too?

Yes it is. Short for Ignacio.

Oh wow. I'm going to change my name to Ignacio so people can call me Nacho. :p

Luís = Lucho
Patricia = Paty
Eugenio = Queno
Fernando = Nano
En Italia es más compleja la cosa:
Giovanni=> Vanni=> Vannino=> Nino=> Ninino.
Cosimo=> Cosimino=> Mino=> Mimino.

Yes, but those aren't as neat because they don't sound like nachos. :D

Nano is definitely a dimutive, in more ways than one. :D