There are two formulae you can use to introduce yourself:
Me llamo … – My name is… .
Soy… – I am … .
In order to introduce somebody you can say:
Mira, este es.../esta es... – Look, this is…
Or, more polite
Mire, este es.../esta es... – Look, this is…
In a formal context, use encantado (masculino) or encantada (femenino) to say Nice to meet you. In Latin America you can use the formula Mucho gusto which is invariable.
In an informal context, just use ¿Qué tal?
– Hola, soy Ana.
– Yo soy José, encantado.
– Encantada.
If you missed the name of your interlocutor, you can ask her again:
Perdona, ¿cómo te llamas? – I´m sorry, what is your name?
Or, more polite
Perdone, ¿cómo se llama? – I´m sorry, what is your name?