If you use referenced Selectable Options exactly like @Ander described, updating the source will automatically update the references. So if you need just the names (Text values) that works.
But even if you need to reference the full row, to be able to fetch other properties, Select List still works. Actually Lookup From Table is nothing more than a Select List with restricted Selectable Options.
Seeing as your “Unique” name column is not unique at all, the question is what column do you want to reference when you select it through Lookup from table? You probably need to rethink your schema a bit.
As it stands, you can either create another table like Ander showed just above, or you make your Unit Type column a Select List, then use the following formula for Selectable Options. It will fetch the first row of every “unique” set of rows.
[Unit Data Table].Filter([Unit Data Table].Filter([Unique Unit Name]=CurrentValue.[Unique Unit Name]).Find(CurrentValue)=1)