Hi Haki Saki,
Regarding this issue, I tried to replicate this issue at my local but I can't reproduce this issue. I've also tried at your site by creating a test group and give the permalink 'test-group-one'. After the group created, i then change the permalink to 'test-group-two' and I don't see where is the duplicate avatar / cover. Can you tell me what is the steps to reproduce this issue? If can, maybe you can capture a screenshot and show us the issue?
Please advise.
Hope this help and have a nice day!