Absolutely. You can however, if you so wish, once you have your French nationality ask for it to made "Francisation" which means that your Polish name which ends in Ski or Sky or Xyz and your unpronounceable (not to mention spellable) first name can be made into a French name. I believe that you can choose from several French first names, although the last, or surname, is closest to the original as possible. Perhaps simply by knocking off the last three letters and all the accents over the vowels
- I'm on a roll here, lads.
When you go civilian You must have your original name back, unless you have naturalization as in the case above. Which is why in the Képi Blanc magazine you do get from time to time Leg 1st class X or Cpl X or even Sgt X, who is going civil and is outside the museum for the official photo.
That is basically because the person, for whatever reason, does not want people to know that he was in the legion.