How do I rename startup manager entries?

Usually the name of the macOS boot volume is what should be displayed on the boot picker menu. What ever name you give the macOS boot volume in the Finder should show up on the Apple boot picker menu when Option Booting the Mac.

As for the Ubuntu volume, you will need to "bless" the Ubuntu bootloader as suggested by @fobya. First you need to mount the hidden EFI/ESP partition where the Ubuntu bootloader is stored. Launch the Terminal app and mount the hidden EFI/ESP partition:

diskutil  mount  disk0s1

Now run the "bless" command:

sudo  bless  --folder  /Volumes/EFI/EFI   --file  /Volumes/EFI/EFI/ubuntu/boot_x64.efi  --label  "Ubuntu"  --shortform  --verbose

Now the above command may be incorrect since I'm not sure what name Ubuntu gives their bootloader on a Mac. Ubuntu may be using "grub_x64.efi" instead, so the command would instead become this:

sudo  bless  --folder  /Volumes/EFI/EFI   --file  /Volumes/EFI/EFI/ubuntu/grub_x64.efi  --label "Ubuntu"  --shortform  --verbose

Then unmount the hidden EFI/ESP partition:

diskutil  unmount  disk0s1

Just verify I have the proper path listed as I am doing this from memory.

You need to make sure the path to the "boot_x64.efi" or "grub_x64.efi" file is correct in my commands. If the path is correct, then you may need to change the "folder" option to "/Volumes/EFI/EFI/ubuntu" instead. It has been a while since I used the "bless" command so I am not certain which folder is necessary (verify the folder is actually "ubuntu" as well).

If it still doesn't work, I wonder if you need to temporarily disable SIP from Recovery Mode:

csrutil  disable

Just remember to re-enable SIP or bad things could happen to macOS:

csrutil  enable