I really don't want to be nitpicky, because the story is really good and this really doesn't matter but "Para llamar mi propia estrella" does not mean "To call a star my own".
It actually means "To call my own star". If you wanted that sentence in Spanish, you'd say "Para llamar una estrella mía".
I guess the confusion went with what's subject and what is object. When we learn another language, we're told that the order is fixed, but that's just not the case in Spanish nor is it in English.
The taught order would be "A Star to call my own" or "una estrella para llamarla mía". The -la at the end of the verb is doing an implicit it, "...to call it my own". But you can rearrange the sentence to verb + subject + object and keep making sense. But what they did was verb + object + subject. Which you could also do, but it'd look like this:
"Para llamar mía una estrella"
The word "own" becomes redundant and it vanishes. Keep it and you change the meaning. And the word "una" is missing too. That article is necessary to separate the subject from the object.
Other alternatives:
"Para llamar a una estrella mía".
"Para llamar a Estrella mía". in this case, Estrella becomes the name of something or someone.
"Para llamar una estrella la mía". The article la here comes with the implicit meaning that it's common place to have a star, but the protagonist doesn't have one and the story is about how they get their own. And I say they, because the gender of the word "mine" in Spanish refers to the object in question and not the person to whom it belongs. "La estrella es mía", "el sol es mío".
"Mi propia estrella para llamar". My own star to call. Pretty much the same implicit meaning in both languages.
"Para llamar mía propia una estrella". I said it was redundant. But you can use redundancy to make emphasis. It matters, like really matters to the protagonist that they can get a star to call theirs.
But that's the thing, we say "mine own", not "my own". "Own" is a word for emphasis.
