Is this no longer possible? All information I've read about it ends up pointing to broken links. I opened a help ticket in-game, but the GM gave me a brush off answer to check the website, which I've obviously already done.
As to your question on buying a name change with Turbine Points. No idea if the change credit is assignable to any character. Rumor has it that you can buy a change credit with a freep character. Assign the credit to one of your creeps. Rename your creep. Like I said, no idea if this mechanism works. Since there are no refunds for LOTRO store purchases, without some assurance that it is supported from a Turbine employee - perhaps not a good idea.
Unless stated otherwise, all content in this post is My Personal Opinion.
I sent in a support ticket on the website, but none of the categories of question were applicable. If you select "Premium Services", it only speaks about Renaming Kinships, and Server Transfers. Hopefully I can get an answer in a reasonable amount of time.
I'm actually shocked at the lack of information regarding this stuff. For all the content on the Lorebook site, the actual Turbine site and FAQ are horrid.
I can confirm, when you buy the Store-purchased Rename, it asks which character you'd like to use it on. Hopefully this thread gets indexed by google, and can serve as a reference for others in the future!