Tnneya is the lover of Mrrungo-Mu. She is given special previledges that others are not allowed. She deeply loves Mrrungo but not what he has become, a power hungry tyrant.
She attempted to escape from Mrrungo and was able to take her personal ship without his permission. When he learned of this, he sent a ship after her.
Through a dream, the Silver Surfer knew the location she would be in. He stopped them from taking her. They destroyed their own ship rather than face Mrrungo and his wrath.
Tnneya was able to trick the Surfer into believing that she was Shalla Bal. Her power is to make others believe she is their one true love. The Surfer eventually saw through this and went to Mrrungo in order to save Shalla and all those captured by the Enslavers.
When Mrrungo was defeated, Tnneya pleaded for the life of Mrrungo. They left in part of their massive ship together, most likely to lead a normal life once again.