You would place the exact name as it appears in /boot/grub/grub.cfg (between the quotes). An example might look like:
It appears that you can do the same thing via Grub Customizer: Edit > Preferences: General tab. Click on 'default entry' > predefined. Click on the 'entry 1' selection box. It will expand; select the name from the right column. Click 'Save' to configure Grub 2 according to GC's scripts.GRUB_DEFAULT="Ubuntu, with Linux 2.6.35-28-generic-pae"