Meaning of Ephesus. Israeli name. In Israeli, the name Ephesus means-desirable.The name Ephesus originated as an Israeli name. The name Ephesus is most often used as a girl name or female name.Israeli Name Meaning-desirable.Origin-Israel.sraeli name. In Israeli, the name Ephesus means-desirable.The name Ephesus originated as an Israeli name. The name Ephesus is most often used as a girl name or female name.