If your parents are dead, do you still include their name in a wedding invitation
You do not word your invitation as if your parents are sending them. You word them something like: Mary Doe, daughter of the late John and Sue Doe and John Smith, son of Tom and Jane Smith... etc,
Yes. There are statements you can use to indicate that they are deceased if that is your wish.
You will still include their names in the wedding invitation. Many grooms and brides acknowledge their deceased parents during their wedding day, with a loving and caring tribute in the wedding program or poem recited in their memory too.