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Does accidental notes have their own name?

So if I understand correctly in western tonal music we chose 12 notes that we use , among which we have named 7 notes as follow :

  • C - D - E - F - G - A - B, or;
  • Do - Ré - Mi - Fa - Sol - La - Si (how we call them in France) or I heard as well;
  • Do - Ré - Mi - Fa - So - La - Ti

The other 5 get the suffix 'sharp' (#) or 'flat' (b), like so :

  • C# - D# - F# - G# - A# or; in their flat version;
  • Db - Eb - Gb - Ab - Bb or;
  • Do Dièse - Ré dièse - Fa dièse - Sol dièse - La dièse (french);
  • Etc...

Is there an historical reason for naming accidentals rather than assigning a letter-name to every pitch?