A girl was born to parents that were separated or perhaps already divorced. When it came time to name the baby the side of the Mother wanted one name and the side of the Father wanted another name. They both went to shul and “gave the name” they wanted. And proceeded to call her by both names (each side by their name.) For example Rivka and Bracha…
Someone asked in such a (rather funny) situation what would her name be for in regards to writing a get? Would they put down both names?
It is unlikely that she’ll get divorced, after the trouble that her parents’ divorce caused her!
If this rather hypothetical person does get divorced, then the main name will be the main name (assuming that in school and so on she is called by one main name), and the other name, if it is still in use, will be added as an “extra name.”
Names are not decided by aliyos in shul, but by what the person is actually called.