You may not see it often, but it does come up as a way for someone to give their name.
More specifically, it’s like saying, “I’m called —”.
Here's an example from another manga, where a character introduces her friend.
It's also seen with kanji, as in this scene where an aquarium employee tells the name of an otter.
When someone gives a name this way, it often ends with の or similar. This is because this use of の has a grammatic use of explanation.
って is another way to say と, and so you may see this written as と言う and という as well.
Note that 「nameと言う」 translates as “called ‘name’” and this can be used to state what something is called aside from a name.
Regarding Mia’s line, she’s saying, “Is called Mia.” The pronoun is left unspoken, but from context, we can tell she’s referring to herself.
This is not unlike someone in English saying, “The name’s Scott.” The speaker can be saying his name is Scott, or he can be answering someone asking his son’s name, or his pet poodle’s name.
Context helps fill in the “who” that is called the given name or word.
You get used to it with exposure (reading and more reading) and experience (learning along the way).
Although there’s no rush to learn them now, over time, you will encounter:
- 私
- あたし
- 僕
- 俺
…and many others. (Some characters use うち is used as a pronoun.)
There are different pronouns used to refer to oneself. Some are typically used by boys, and others are typically used by girls. Some are more feminine (あたし), and some are masculine (俺).
I mentioned this above, but you’ll find that the と used for quoting often is spoken as って.
It may seem confusing at first because it seems like it’s acting like the て form of a verb, but you’ll get used to it over time. When you see a noun or clause with って attached to it, that means it’s being quoted (either a direct quote or an indirect quote).
This っていう thus is short for と言う, but you may also see って by itself being short for と言う.
If you search the thread for っていう, you can also see prior discussion on it:
I guarantee that with enough reading experience, you’ll look back on this and say, “It’s so clear and obvious this girl is giving her name.”
There’s a first time for learning everything, and I know I sure went through my share of spending time trying to figure out the basics. It’s all part of the learning process!