Learn German: Mein Vorname ist Anna. - My first name is Anna.

Possessive words like "my" change their endings based on the gender of the noun they belong to. Vorname is a masculine noun (der Vorname). Since it is the subject of the sentence (the nominative case), the masculine form is just Mein with no extra ending. If it were a feminine noun, it would be Meine.

What is the difference between Vorname, Nachname, and just Name?

Vorname literally translates to "before-name" and means "first name". Nachname means "after-name" or "last name". If a German person just asks for your Name, they usually want your last name (or your full name). This sentence specifically points out the first name.

Would I normally introduce myself by saying Mein Vorname ist Anna?

Usually, no. This phrasing sounds very formal or technical. You would use it when clarifying paperwork, checking in at a hotel, or speaking to officials. In normal social situations, it is much more natural to introduce yourself with Ich bin Anna or Ich heiße Anna.