procedure DoRequest;
var
  Http: TIdHTTP;
  Params: TIdMultipartFormDataStream;
  RequestStream, ResponseStream: TStringStream;
  JRequest, JResponse: TJSONObject;
  url: string;
begin
  url := 'some_custom_service'

  JRequest := TJSONObject.Create;
  JResponse := TJSONObject.Create;
  try
    JRequest.AddPair('Pair1', 'Value1');
    JRequest.AddPair('Pair2', 'Value2');
    JRequest.AddPair('Pair3', 'Value3');

    Http := TIdHTTP.Create(nil);
    ResponseStream := TStringStream.Create;
    RequestStream := TStringStream.Create(UTF8Encode(JRequest.ToString));
    try
      Params := TIdMultipartFormDataStream.Create;
      Params.AddFile('File', ceFileName.Text, '').ContentTransfer := '';
      Params.AddFormField('Json', 'application/json', '', RequestStream);

      Http.Post(url, Params, ResponseStream);
      JResponse := TJSONObject.ParseJSONValue(ResponseStream.DataString) as TJSONObject;
    finally
      RequestStream.Free;
      ResponseStream.Free;
      Params.Free;
      Http.Free;
    end;
  finally
    JRequest.Free;
    JResponse.Free;
  end;
end;

var
  s: String;
begin
  s := EncodeHeader('Επιστολή εκπαιδευτικο.docx', '', 'B', 'UTF-8');
  ShowMessage(s); // '=?UTF-8?B?zpXPgM65z4PPhM6/zrvOriDOtc66z4DOsc65zrTOtc+Fz4TOuc66zr8uZG9j?='#13#10' =?UTF-8?B?eA==?='
  s := DecodeHeader(s);
  ShowMessage(s); // 'Επιστολή εκπαιδευτικο.docx'

  s := EncodeHeader('Επιστολή εκπαιδευτικ.docx', '', 'B', 'UTF-8');
  ShowMessage(s); // '=?UTF-8?B?zpXPgM65z4PPhM6/zrvOriDOtc66z4DOsc65zrTOtc+Fz4TOuc66LmRvY3g=?='
  s := DecodeHeader(s);
  ShowMessage(s); // 'Επιστολή εκπαιδευτικ.docx'

  s := EncodeHeader('Επιστολή εκπαιδευτικ .docx', '', 'B', 'UTF-8');
  ShowMessage(s); // '=?UTF-8?B?zpXPgM65z4PPhM6/zrvOriDOtc66z4DOsc65zrTOtc+Fz4TOuc66?= .docx'
  s := DecodeHeader(s);
  ShowMessage(s); // 'Επιστολή εκπαιδευτικ .docx'
end;

with Params.AddFile('File', ceFileName.Text, '') do
begin
  ContentTransfer := '';
  HeaderEncoding := 'Q'; // <--- here
  HeaderCharSet := 'utf-8';
end;

with Params.AddFile('File', ceFileName.Text, '') do
begin
  ContentTransfer := '';
  HeaderEncoding := '8'; // <--- here
  HeaderCharSet := 'utf-8';
end;