The story of Theseus lifting the rock to claim his father's sword reminds us a lot of a couple other famous stories. The closest one is probably the story of King Arthur, who in some versions proves he's the son of the former king, Uther Pendragon, by pulling a sword from a stone. In other versions, he is given the sword by the Lady of the Lake who emerges from (you guessed it) a lake to give it to him. Either way, just like Theseus, young Arthur claims a sword before pursuing his destiny as a great hero and king.
Another famous figure who did some sword-claiming was a dude named Sigmund, who appears in Norse/Germanic mythology. Sigmund is attending a wedding, when Odin, the king of the gods, appears disguised as a beggar and stabs a magnificent sword into a tree. Odin says that whoever can pull the amazing sword from the tree can have it. The hero, Sigmund, is the only person who can manage it, and the sword serves him well in tons of adventures. Later on, the sword is shattered, but it's reforged by Sigmund's son, Sigurd, who uses it to slay the dragon Fafnir. Like Theseus, Sigurd claims the sword of his father before running off to be a big time hero.
This claiming of the sword thing has also made its way into tons of modern fiction and movies. For example, there's Aragorn of J.R.R. Tolkien's The Lord of the Rings, who re-forges Narsil, the sword of his ancestor, Elendil, on his road to claim his rightful place on the throne of Gondor. Another big example is in Star Wars when Obi Wan Kanobi gives Luke Skywalker the lightsaber of his father Anakin Skwalker, aka Darth Vader. Armed with this sword, Luke heads off to defeat the evil Empire.