At this moment right now, it is important to make sure that you can access the domain name, have the ability to renew it, and keep your hosting active.
THEN worry about the theme - providing you have access to the domain name etc, then you also need to make sure you have COMPLETE ADMIN RIGHTS on the wordpress website - it maybe a case that your designer give you limited rights in the admin area.
A question had been raised similar to your own predicament -
Q: If a Theme was purchased by a ‘web designer’ and the ‘end customer’ now wishes to take ‘ownership can the licence be transferred to them ? A: Since download and purchase processes are managed by Envato, i believe it would be the best if you contacted them. Even if to transfer a license would be possible, your client probably would need to provide copy of the license or some sort of proof. I hope it works out!
From what I can see unless you can provide the evidence needed, then my best suggestion would be for you to buy the theme
And then enter the new licence key and information in your name. At least you will also be entitled to 6 months of support