Look in /etc/grub/grub.cfg :
for proxmox entry , similar to this :
menuentry 'MB Recover Proxmox VE GNU/Linux' --class proxmox --class gnu-linux --class gnu --class os $menuentry_id_option 'gnulinux-simple-ddfe9089-a176-4112-9515-0ad598ae2ad8' {
load_video
insmod gzio
if [ x$grub_platform = xxen ]; then insmod xzio; insmod lzopio; fi
insmod part_gpt
insmod lvm
insmod ext2
set root='lvmid/j2PveR-z1u1-8OR2-gnO9-OysQ-N49j-ZtJ3Aa/mTy7eR-xW1D-kiGQ-qhDj-CeVm-1ecH-jTeAHH'
if [ x$feature_platform_search_hint = xy ]; then
search --no-floppy --fs-uuid --set=root --hint='lvmid/j2PveR-z1u1-8OR2-gnO9-OysQ-N49j-ZtJ3Aa/mTy7eR-xW1D-kiGQ-qhDj-CeVm-1ecH-jTeAHH' ddfe9089-a176-4112-9515-0ad598ae2ad8
else
search --no-floppy --fs-uuid --set=root ddfe9089-a176-4112-9515-0ad598ae2ad8
fi
echo 'Loading Linux 6.8.12-4-pve-mb ...'
linux /boot/custom/vmlinuz-6.8.12-4-pve-mb root=/dev/mapper/pve-root ro quiet
echo 'Loading initial ramdisk ...'
initrd /boot/custom/initrd.img-6.8.12-4-pve-mb
}
copy the enty to /etc/grub.d/40_custom
change initrd and linux to your image and kernel name
copy existing images and kernel to your name into a new dir under /boot
mkdir /boot/custom
cp /boot/vmlinuz-6.8.12-4-pve /boot/custom/vmlinuz-6.8.12-4-pve-mb
cp /boot/initrd.img-6.8.12-4-pve /boot/custom/initrd.img-6.8.12-4-pve-mb
then
update-grub
check /etc/grub/grub.cfg for the entries