Is it common for parking garage attendants to write down license plate numbers and why would they need to write it down? I didn’t see him write down other license plate numbers on the time ticket.

Typically people who lost their ticket, cant pay for their ticket, the driver is driving a commercial vehicle and performing a service in the garage like fixing a flat tire, or perhaps a city vehicle coming out. If anything sketchy seems to be going on no matter where you work or live it only makes sense to take down information that's avaliable to the public.

I've never seen this happen before. I've been parking here for some time.

Not common. Been going there for years and i never noticed anyone doing that.