Yes, but not always. And I want it to say my first and last name as the default. Right now I'm in a zoom meeting where my video is not displayed, but I'm able to write in the chat. I want my first and last name in there too - but there's nowhere to change it.
Changing your display in your web settings will not change your name within a meeting in progress.
You have to rename yourself within the meeting, if it is allowed by the Host - which it isn't always.
Right-click yourself in the meeting and choose rename there.