Harsomtus is the Greek form of the Egyptian name Her Sema Tawy, which means "Horus, Who Unites the Two Lands".
Background to his name is the ancient symbol of uniting Upper-Egypt (the Nile valley) and Lower-Egypt (the Delta), originally two separate countries; this unification took place more than once in Egyptian history, for the first time by the mythological king Menes and later at the end of each Intermediate Period.
The unification was illustrated (for example on the sides of the throne) by tying the papyrus and the lotus plants (symbols for the two countries, in Egyptian tawy) around the hieroglyph sema, "uniting", by Horus and Seth (to whom the two regions had been given) or also by two Nile gods (Hapy). King Montuhetep II (11h dynasty) changed his Horus name in Sematawy after reuniting the two countries.
Harsomtus was the son of Horus and Hathor or Isis, and as such could be exchanged with the god Ihi in Dendera.