If you are already signed in to ZOOM app, just click on your user icon, and click on settings.
This will open below settings page, click on below highlighted “view more settings”
This will take you to web page where you can change your first name and last name.
Simply login to https://zoom.us/profile
then click Personal > Profile > Name > Edit
Enter your first name and last name, as soon as you hit save, it will reflect in your zoom client also.