Hebrew names spelled in English are still Hebrew names. For instance, the Poster above remarked that her daughter’s “English” name, Abigail, was selected because it starts with the same phoneme as her Hebrew name, Avigayil. Abigail and “Avigayil” are the same name. Her Hebrew name and her “English” name are the same, just spelled in different alphabets. Many people in America have Biblical (I.E. Hebrew) names. Some of them might sound silly to us like Nimrod or Balaam but, nevertheless, they are Hebrew names, just spelled in English. Also note that using a name from the local culture or language in addition to one’s Hebrew name is not a modern phenomenon. The practice goes back to Golus Bavel, for instance, the name Zerubavel isn’t Hebrew. Many of the Chachmei haGemorah had both Hebrew and Aramaic names.
P.S. Phineas is actually Latin for Pinchas.
P.P.S. An alternative to anglicizing Hebrew names is to just use the initials. My name is Alter Yoseif but in English i’m just A.J.