I am going to replace (buy new UTM) old UTM - Endpoint have been deployed to 10+ desktops.
Do I have to re-install endpoint software on each desktop to "link them" to new UTM?
No, as long as you restore the backup from the old unit to the new unit. The UTM-ID is saved in the configuration backup file, not tied to the actual hardware. If you create a new configuration from scratch on the new UTM, then yes, you would have to re-deploy.