To make a permanent change to the display name, log onto the Zoom.us .web page for your account. Notice the text in small font on your Profile tab, circled below in the middle of the screen:

Click the Edit button on the right side to make a “permanent” change by editing the Display Name which is highlighted yellow here:

It’s “permanent” until you come back here and change it. If you change it anywhere else in Zoom, it’s only for that session – as you’ve discovered.