5-15 year olds can be the named cardholder on a Disabled Persons Railcard, but as child fares aren't covered by the card it means that only the adult with them would get the discount until they’re 16. The adult would need to apply using the child's name, as this is the name that needs to go onto the card and the adult would only need to put their name into the payment section of the application.
The best option for children with a disability under16 years old would be to purchase the 'Family and Friends Railcard' as this would cover the adult travelling with the child but also give them an extra 60% off the child fare.
Click here for more info about the Family & Friend's Railcard