The ability to rename your kinship has not been available for some time. I wasn’t even aware this was an option so I cannot speak as to when the option was closed. Today CarpeNoctem on the forums has announced their return and a significant price change!
We are pleased to announce that Kinship renames are again available. Previously, players had to pay $12.95, €11.49, £9.95 or 1550TP for these renames, but there will no longer be a cost associated with them! These will be offered free to players who are either VIP, or Premium players have purchased Turbine Points within the last 45 days.
To submit a Kinship rename request, the Kinship leader will need to submit an In-Game support ticket by pressing Esc while logged in, and then going to the Help options.
Yup, free! I wonder if it was just low enough volume that Turbine is ok with helping without cost. It’s still a very nice service they are offering for free.
I’m not certain if this means it is still available for pay options if you are not a kinship leader that falls into those two player categories. It sounds like it’s free but if you aren’t VIP, you’ll have to have purchased some Turbine Points.
Source: LOTRO Forums