Learn Spanish (Spain): ¿Dígame? Hola, soy Ana.

In Spain, it is very common to answer the phone by saying ¿Dígame? or simply ¿Diga?. Even though it literally means "tell me", it is the standard way to say "hello" when picking up a call.

What is the exact grammar behind the word "dígame"?

It is a command form of the verb decir (to say or tell). It combines diga (the formal usted command for "tell") and the pronoun me (to me) into a single word.

Why does she say "soy Ana" instead of "es Ana"?

In English, we use "it is" on the phone to identify ourselves, as in "Hi, it's Ana". In Spanish, you do not use a direct translation of "it is". Instead, you literally say "I am Ana" by using soy Ana.