All installs of Ubuntu use one UEFI entry 'ubuntu' and many unofficial flavors alsp use same entry if based on Ubuntu. All installs must be UEFI, not old BIOS.
Last install is normally the grub in control, if you want another grub in control, boot into it and do sudo grub-install. That resets the UUID in the ESP to that install's UUID. You can manually edit UUID, but permissions on ESP are restricted by settings in fstab.
Windows often is similar in that you have one BCD in control that lets you choose one Windows or the other. Some reconfigure with another temporary ESP, to have 2 BCDs, so grub can directly boot either Windows install.
You can see UEFI boot entries with, UEFI uses GUID of ESP to know which partition to find boot files:
sudo efibootmgr
And you can see UUIDs & GUIDs.
lsblk -e 7 -o name,fstype,size,fsused,label,partlabel,mountpoint,uuid,partuuid
Since 14.04 fstab has mounted ESP - efi system partition with no permissions (0077). (shows my UUID only as example.
UUID=68CD-3368 /boot/efi vfat umask=0077 0 1
Prior it used defaults, but was then not as secure:
UUID=68CD-3368 /boot/efi vfat defaults 0 1
You can mount ESP from live installer to see three line grub entry which uses the UUID to find grub.cfg in default install. If fstab has correct ESP mounted then update grub in any other install will update UUID. Not major updates in second install may redo it as default & you have to reset to your preferred install
Example 3 line grub configfile in ESP, the UUID 75f... is UUID of my install root partition on nvme0n1p6 (hd0,6). And in install ESP is mounted at /boot/efi
fred@dell5310:~$ cat /boot/efi/EFI/ubuntu/grub.cfg
search.fs_uuid 75f21d9b-d206-4e74-afc3-f44ac6c4a583 root
set prefix=($root)'/boot/grub'
configfile $prefix/grub.cfg
If for some reason I get grub> and either remember or use ls to find grub.cfg, can use configfile to boot as above but one line.
configfile (hd0,gpt6)/boot/grub/grub.cfg
I have tried getting different UEFI entries, by editing /etc/default/grub, but find Ubuntu's grub is hard coded to use /efi/boot/grub.cfg in ubuntu folder. I do get new folders in ESP with new name and new UEFI entries, but it does not use grub from that folder just ubuntu folder.
This user said it worked for him.
How do I install two independent Ubuntu installations on a single hard drive with UEFI?