Formal:
* Меня зовут Елизавета. (Menya zovut Yelizaveta.) - This is the most formal and polite way to introduce yourself. It literally translates to "I am called Elizabeth."
* Я Елизавета. (Ya Yelizaveta.) - This is also formal and means "I am Elizabeth."
Informal:
* Меня зовут Лиза. (Menya zovut Liza.) - This is a more casual way to say "My name is Elizabeth," using the shortened version of the name.
* Я Лиза. (Ya Liza.) - This is also informal and means "I am Liza."
You can choose the best option depending on who you are talking to and the situation.