If “ownership” implies choice or agency, then most of us didn't truly "own" our names initially. They were given to us without our consent, and we often grow into them as labels rather than consciously choosing them.
In a practical sense, the name assigned at birth is more like an identifier that links us to legal rights, responsibilities, and records. It’s a part of our legal identity rather than something we “own” in a personal or autonomous way.
However, legally speaking, your name functions as an anchor point for your identity within society. So even though you might not “own” it in a traditional sense, it becomes part of your identity that you have the right to use, change, or protect, especially if you do later choose to adopt it fully.