When create issue is called with a project name that doesn't exist, the error indicates that project name is not specified instead of project doesn't exist.

{
  "summary": "This is a test issue",
  "description": "This is a test description",
  "category": {
    "name": "General"
  },
  "project": {
    "name": "mantisbt2"
  }
}

Result:

{
    "message": "Project not specified",
    "code": 11,
    "localized": "Ein notwendiges Feld „project“ war leer. Überprüfen Sie Ihre Eingabe."
}