One book of mythology that I read claimed that Theseus derives from thēsauros (θησαυρός), a word meaning “treasure” or “deposit”, and that the name was given to him because his father King Aegeus deposited his sandals and sword under a stone for Theseus to find when he grew up, to prove himself as Aegeus’ son and the heir to the throne of Athens.
Theseus's adventures didn't stop once he returned to Athens. He sailed on the Argo with Jason, Orpheus, and cousin Hercules. He also traveled to the Underworld with his friend Pirithous, who wanted the goddess Persephone (Hades's wife) for his own, and both men were put into Chairs of Forgetfulness. Theseus was rescued by Hercules, but Pirithous had to remain because the Lord of the Underworld knew that it was he who instigated the attempted kidnapping of his wife. Later, when Hercules had slain his wife and children while in a blind rage given to him by Hera, Theseus attempted to console his cousin by "sharing his guilt" and brought him back to Athens. However, Hercules felt that he needed to be truly punished and set off for his Twelve Labors. It is said that Theseus also set up the first democracy.