The way to rename a RAID array and make Ubuntu persist the name change across boots is to rename the device and update your initramfs.

First rename the device:

sudo mdadm --stop /dev/md125
sudo mdadm --assemble /dev/md/alpha --name=alpha --update=name /dev/sd[fg]
sudo mdadm -Db /dev/md/alpha

The third command should return something like:

ARRAY /dev/md/alpha metadata=1.2 name=omicron:alpha UUID=5b024352:3a940335:233aa23f:5c6b2a1f

Paste the result into /etc/mdadm/mdadm.conf (replacing the old line). Or execute:

sudo mdadm -Db /dev/md/alpha >> /etc/mdadm/mdadm.conf

After updating your array name and mdadm.conf, you need to issue the following command:

sudo update-initramfs -u

Finally, reboot.