If it were I, I'd simply buy another unit, but contact the supplier/manufacturer first & see if there's any chance of replacement from their end. Nowt to lose by asking. Obviously, get new nuts next time.
I personally wouldn't risk messing around with that.
I'd sooner run a damaged M8 thread than any of the M6 options. @Agroshield 's suggestion of a tube nut to sit inside the top mount is probably the best solution on offer, assuming you can modify the top mount to accommodate it. It was used in a lot of kits for fitting mk2 top mounts to mk1 mx5 dampers from vendors of variable quality and I don't recall any reports of failures.
I was thinking with a die. No actual threading on the lathe.
The lathe work just involves removing the old thread (all of it), reducing in diameter so the weld interface is not involved in the new thread, and then making the weld build up into an 8mm diameter cylinder.
With the nitrogen warning above, it might be wise to have the shock in a bucket of water or a wet rag around the shaft when welding it up.
You could do the (final) turning without a boring head. Hold a lathe tool in the four jaw and set it to touch/stratch the shaft on a part below that which you have repaired. Then wind the carriage towards the tailstock.
M7 would be less of a change, plenty of nuts available, I bought some from my local motorbike workshop (M7 is common on some exhaust studs - Piaggio etc..)
Most of the load will be when the shock compresses so no load on the nut then, the nut is only used when the shock extends.
Is this for a gently driven town car or a competition off-roader?
I have adjusted the shock absorber as short as it will go. It is now far shorter than factory and I suspect that it will affect the handling. The rear unit must have the spring seat set too high but it (although threaded) claims not to be adjustable.
The suppliers are highly unlikely to be helpful in my experience of not putting their hands up.
Run a die down over that to clear up damage and fit two nuts. Or a long nut as posted before. The damaged bits will reduce the strength of the fastner but a double nut will more than compensate.
Leaving the burrs in place risks damaging the nut on the way on and then the threads moreso on the way off again.