Irish versions of Eugene:
Éogan or Eógan is an early Irish male name, which also has the hypocoristic and diminutive forms Eoganán, Eóghainin, Eóghain and Eóghainn. In more modern forms of Irish it is written as Eóghan or Eoghan (/'oːəun/).
Above from wikipedia.
Perhaps Eughit is what the compiler of the register thought they heard.
Tony
