Mentioning your famous relatives to your coworkers: good idea?

One of my coworkers does Zoom meetings from the coworker’s living room. There is a painting of a person in the background. If you ask the coworker who it is, the coworker mentions who it is: ”my grandfather when he was young”, and mentions the name: a very prominent American, just at a relatively young age.

OK, so my coworker is from a famous and wealthy family.

Bad idea for the coworker to put the famous relative’s portrait in the background on Zoom meetings? If not, bad idea for the coworker to mention the famous relative’s name? The coworker could simply say, “it’s my grandfather”, without saying a name.