I was told a while back by ASM development that the ASM cookie name format is TSxxxxxx where the x's are six hex characters generated from the web app (httpclass) name. So if you're seeing multiple ASM cookies being set in the same response, I'd expect it's because there are multiple ASM web applications in the response chain. As you've said that's not the case, I'm not sure what would explain the variety of ASM cookie names.
Someone from F5 mentioned you have a case open on this. I expect they'll be able to help you investigate this. If you don't mind, can you post the explanation once it's determined?
Thanks,
Aaron