Her name didn't matter. In the grand scheme of things.
On a personal level, of course it mattered to her. It was her name, after all. Your identity, your personality and your soul, they are linked to your name.
And certainly there were plenty of government departments and businesses that wanted her name recorded and kept, either to prevent fraud or to sell her things, and that wasn't totally separate in both cases.
The records should have her name, yes. But it's not that important. Once she stood up to the troops and was shot, her name became somewhat irrelevant...