It isn’t a matter of “not understanding”: naming conventions have a legal component. I assume it is at the state level. For example, I wanted my children to have my last name in their names, but I didn’t want to do a hyphenated last name, so legally they have two middle names: the “given” middle name, and my birth last name.
I work in health care, and we have many Latinx patients with traditional naming formats. The way we use their name on documentation, and in addressing them is however they have reported it to us when they became our patients.
You do have the right to have whatever name you want, but be aware that without a hyphen, it may not legally be considered a surname.