Dogecoin, the cryptocurrency, is not trademarked, and therefore does not have an official owner.
The creators introduced Dogecoin in 2013 and formed a nonprofit called the Dogecoin Foundation in 2014, but they only just applied for the trademark in August of this year, according to the U.S. Patent and Trademark Office. In fact, others filed for the trademark months before the Dogecoin Foundation did.
As of right now, no one has the rights to the name in the U.S. or the E.U., and it remains to be seen who will get them.