I would like to display a different name of these items - that would indicate for example that one is windows partition, other ubuntu, etc.
Is it feasible?
Yes, but not through thunar. Mapping a name directly with partition is something that not even supported by dolphin.
What you should do is add a disk label instead, for linux ones, use
For windows one, just boot into your Windows and rename it in
Meanwhile, in a different circumstance, as I was managing partitions in Gparted, I noticed the option 'Label' that could be accessed for unmounted partitions
This label is the one in Thunar's side pane. Any partition, including Windows can be renamed in this way.