No the neutral is fine how it is. You will just need to make sure there is no bonding jumper that goes from the ground bar to the neutral bar in the sub panel. You don’t need to run a ground back to the main ground. What you have to do is to have the subpanel isolated between neutral and ground so that they are not bonded there. You can drive a ground rod near your subpanel and have that as your ground for your subpanel but again making sure your subpanel is not bonded with the neutral bar.