My son was not offered place is RGS-HW that was our first choice, may be because of distance!
What are the chances if we put his name in waiting list?
We leave in Bracknell. Around 15/16 miles from RGS-HW.
Yes, it will have been because of distance. The last place allocated at RGS was to a distance of 7.882 miles (measured as a straight line). You are a very long way indeed beyond that, and I would have thought there is little or no hope of you receiving a place from the waiting list. (It does depend on how many children live between 7.9 miles and 15 miles and who also applied for RGS.)
You can appeal for a place, but as you live a long way out of catchment, you may not have an easy time of it proving to an appeal panel that RGS is the only school that will do for your son. You can read about the Appeal process here: http://www.elevenplusexams.co.uk/appeal ... bed-school
What is deadline by which we need to inform that we want our son's name waiting list? and whom we need to inform?
The information will be in the letter you receive from your local authority. You inform them of any waiting lists you wish to be placed on, and any new preferences you might wish to express. They will then liaise with Bucks CC and you will be told where your son is on the waiting list in around 6 weeks time.
In the meantime you should accept the offered school unless you have a back-up plan.