What is the most logical next event?

How to change your tumblr name
Change your blog name only if you are sure that you are ok with changing the url on your tumblr account.
All links to the former name will be broken. If you share blogs a lot, you may want to consider simply adding secondary blogs in place of a name change.
Decide on the name you want to use in place of your old name. Add a secondary blog to your newly named tumblr account if you want to retain the old blog name.