I know that we can purchase a non-tradeable Pet Slot in the MC now, which used to be something you could only buy with CSC.
I'm curious to know if it's possible there will ever be a similar set-up for renames. :O Renaming pets is always something I want to do, but can never really afford. (For adopted pets with numbers, several underscores, periods, etc.)
[edit] Unless it happens to put a strain on the website if people were to be renaming pets too frequently...
With pet slots, it works because the number of pet slots you can buy from both the cash shop and the MC are capped at a certain amount. Name changes aren't really capped, you can change a single pet's name over and over again.
Your best course of action is to just keep doing quests and buying as you save up money, along with the scraps of CSC you get from the bathhouse pools.