To rename Tag to tag via right-click->rename in Tag Browser you have to first rename it to something else like Tag1. Otherwise the case change is not saved. I don’t believe this was an issue in 7.9, and it does work as expected in the Tag Editor window in Ignition 8.0.7.
On a related topic: are tags in Ignition supposed to be case-insensitive? system.tag.read doesn’t seem to care about case (I had expected it would).