Rudeness almost never allowable from a customer facing employee, but I also think that it's not reasonable to expect that they would tell you their full name. In most cases, a first name and time/location of the encounter is enough to identify someone.

It's just too easy to track down someone's personal information with a full name- it has been known to happen to healthcare providers that are required to post their licensure or wear badges with full credentials. I know a couple of healthcare providers that have been stalked or doxxed, so we have been allowed to not disclose our full names in some circumstances.