Our Gemara on amud beis mentions an opinion of a Tannah, Chanan the Egyptian.  This unusual name actually belongs to two different Tannaim.  This one, our Gemara’s Chanan the Egyptian, has only one teaching mentioned in Shas, having to do with the blood of the goat, should the scapegoat die.  

In any case, the name is of interest.  What Jew takes on the name, “the Egyptian?”  Was he a convert?  Did he come from Egypt originally. I do not know, however there is an interesting responsum from The Maharil (רבי יעקב הלוי בן משה מולין, 1360- 1427, שו״ת מהרי״ל ע״ב ) which discusses these odd Jewish names and derives and interesting halakaha.  Though it is forbidden to explicitly renounce one’s religion even under threat of death, what about trying to pass as a gentile?   

The Maharil says that there is no crime in that, as we see Jews with Gentile sounding affiliations in many areas of Gemara and Tanach, such as Chanan the Egyptian, Uriah the Hittite, and Tzelek the Ammonite, the last two being leaders in King David’s army.  The Amonnites and the Hittites were morally and politically despised, and yet these individuals went by such monikers.  He goes onto to say, if I understood the responsum clearly, that one can even say, “I am a Christian” (obviously, the Maharil didn’t use those exact words as he didn’t speak English), as the word “christ” merely means “anointed”, such as when one christens a boat.  Thus, it is fine to say, “I am a Christian”, as Jews are also anointed, such as the verse in (Psalms 105:15) in which God refers to the Jews, as His anointed, which we say in prayers daily: אַֽל־תִּגְּע֥וּ בִמְשִׁיחָ֑י וְ֝לִנְבִיאַי אַל־תָּרֵֽעוּ.  Of historical note, the Maharil lived in Germany and at that time, one was supposed to declare loyalty to the: “Heiliges Römisches Reich Deutscher Nation”, the “Holy Roman Kingdom, the German people”, and thus for similar reasons, the Maharil allowed one to declare himself part of the “Holy Nation”, because Jews too are referred to as such, (Shemos 19:16): “מַמְלֶ֥כֶת כֹּהֲנִ֖ים וְג֣וֹי קָד֑וֹשׁ”

Also see Ran Nedarim 62b, which seems to offer a similar rationale:

עבדא דנורא אנא. עבד לאיש שהוא כהן לעובדי האש שעבדיו פטורין מכרגא ולא הוי כמודה בעבודת כוכבים דמוכחא מילתא דלא אמר הכי אלא לאפטורי מכרגא וכי קאמר צורבא מרבנן רבותא קאמר דאפילו צורבא מרבנן שרי ליה למימר הכי דהן סבורים לעבודת כוכבים והוא לבו לשמים כדכתיב ה' אלהיך אש אוכלה הוא:
This should be of some relevance in our time of increased ant-semitism and danger, that to try to pass as a Gentile is not forbidden according to the Maharil, and not the same as declaring apostasy.