I have a workaround for this.Sign in (to the same Google account that you are using on your mobile device) on a desktop or laptop computer.
From the left hamburger menu, select Your Places.
Select the tab Saved.
Beside the list Favourites, select Edit list from the three-dot menu on the right.
Write the name of the label in the box provided for each location. Edits will autosave.
This does not appear to work for the list called Starred. I had to delete most of my Starred list and put the places into Favourites. Really I don't know why they bother with the Starred list at all.