Bøgh is a Danish surname.
The name Bøg (Bøeg, Bøgh, Bøegh etc.) is fairly common in Denmark. Though the times families with that name had been living many places in Denmark concentrated in 3 main areas: North-East Jutland, Eastern South Jutland and South Funen/Langeland. In addition several families exist in Norway probably immigrated from Denmark. The name is a form of Old Danish word Bøk or Bok = Beech. In South Jutland the o-form is normally used (Boeg, Boegh), while in the rest of Denmark the ø-form is common (Bøg, Bøeg, Bøgh, Bøegh)