An inquest at Wiltshire and Swindon coroner’s court was opened and adjourned until October 25.
Coroner Grant Davies said police ‘have deemed the death as non-suspicious and there was no third-party involvement’.
Ms Roche had been studying for a degree in English Literature at Durham University.
A spokeswoman added that William and Harry’s cousin ‘will be sorely missed’.
An obituary published by the Yorkshire Post said: ‘Roche, Rosie Jeanne Burke. Died on Monday 14th July 2025.
‘Darling daughter of Hugh and Pippa, incredible sister to Archie and Agatha, Granddaughter to Derek and Rae Long.
‘Private family funeral. A memorial service will be held at a later date.’
The death notice of Ms Roche appeared in The Times newspaper.
The student was a scion of the Barons Fermoy and the eldest child of (Edmund) Hugh Burke Roche, 53, and his wife the former Phillipa Kate