It’s expected that computed columns will not carry over when reusing an existing table with another app.
I explain what I think is happening with RowID’s here. Because the same RowID is maintained behind the scenes, that’s why user specific columns work between both apps.
Not sure about Row Owners. It probably loses the designation but resetting the column as a row owner column should work just fine, unless maybe you are using anonymous emails and you get assigned a different anonymous email in the second app. I’m not sure though.
As for renaming, I’m sure the table name is just a cosmetic thing on the surface. In reality there is probably an underlying ID that is the same in both apps, so it remains as the same table between apps, but the name you see is more than likely tied to the app itself. If a data change from one app is reflected in the other app, then I don’t think you should have a problem.