Note that the Byzantine Rite hymns only apply to the Eastern Orthodox and Byzantine Catholic churches. Its a little silly to say the the Oriental Orthodox must refer to the Baptism of our Lord as the Theophany on the basis of hymns which we may or may not use (actually a blow by blow comparison of the details of how we do the Epiphany or Theophany will make for some enjoyable reading for me this afternoon).
For my part I think Theophany is preferrable in the interests of ecumenical reconciliation, in that as a rule, where possible, the Oriental and Eastern Orthodox should try to share a common liturgical terminology in English, and also the feast is signifigant for the appearance, visbly or audibly, of all three members of the Trinity. At St. Ephraim's Cathedral in Burbank the Baptism of the Lord is depicted with the Holy Spirit descending towards him in the form of the dove, in the frescoes that decorate the altar (which are alas with one exception not really drawn from Syriac aources of iconography).
However I dont think we should be doctrinaire about this. I still often refer to Pascha as Easter in verbal speech as it frankly sounds better in the English language. For that matter, I would have no qualms about calling Pentecost Sunday Whitsunday, so as to diatinguish it from the days of the week that follow, and also from the overall liturgical seasons described by the Pentecostarion. Even within the Eastern Orthodox Church, one of the oldest OCA churches in Alaska is the Cathedral of the Assumption, rather thanof the Dormition, a curious deviation in liturgical language. I believe that cathedral is in Sitka. And for whatever reason the Oriental Orthodox liturgical calendars all refer to the event as the Assumption even though our beliefs about what happened are precisely the same as the Eastern Orthodox.