Disabling multipass icon:
Click on the multipass icon, then select "About", then uncheck "Autostart on login".

(If you think that this option shouldn't be under the "About" menu, leave a thumbs-up emoji in this GitHub issue.)
If you prefer the command-line, you can run:
multipass set client.gui.autostart=false
This option is remembered even after a reboot.
Stopping multipass from running the background:
Merely disabling the icon does not stop multipass from running in the background. If you want to stop it from running in the background (until the next reboot), run:
sudo snap stop multipass.multipassd
To start it again, run:
sudo snap start multipass.multipassd
If you want to disable multipass entirely, without uninstalling it, run:
sudo snap disable multipass
To enable it again, run:
sudo snap enable multipass