I'd put money on 7RHA as the formal NATO-recognised title. They are RHA who happen to be Para, not Parachute Regiment, so I'd suggest more correct would be 7 (Para) RHA, but personally I'd only expect to see the sobriquet "Para" in an expanded title.
7 RHA was officialy re-titled 7th Parachute Regiment Royal Horse Artillery in 1987*, so the "Parachute" part is indeed part of the title, and "7 Para RHA" is the correct abbreviation.
"7 RHA" (and sometimes "7 Para") happens to roll off the tongue better, and so is in common use.
(the then- adjutant John Murphy had the honour of being first to use the title when calling the "re-naming parade" to attention after the CO had made the announcement. If anyone is old enough to remember that day... )
id never expect a para regt bloke to call us 7 Para RHA, just as i call them 2 or 3 bn!!!! correct me if im wrong but it went from 7 para rha, then to 7rha, then back to 7 para rha??? and '7 Para' that does my bloody head in thats not our name