Yes is a random address but later you can change iif you want. Important is that you choose the local self-custody node in advanced mode, not just follow the walk-through default setup.

When you click "advanced" you will see more options to choose which backend LN node you want to use. In case you already by mistake you went by default on cloud setup, in Linux you can delete the .cache/albyhub folder and start over.

Later if you want your own private domain as LN address, you can follow this guide.