I've been living at Jervis Bay on an off for more than 25 years and have been visiting the area since the mid 70's. Heard both versions used extensively and passionate debate about the subject often erupts between those with not much else to worry about.
So when in doubt - turn to Wikipedia!
"Jervis Bay is named after the British Admiral John Jervis, 1st Earl of St Vincent; it was named in 1791 by Richard Bowen. George Bass also entered the Bay when he surveyed the South East coast of Australia in 1797. Jervis was believed to have pronounced his name /?d??rv?s/, but many residents of Jervis Bay (including his descendants) pronounce it [?d???v?s]."
I've always called it "Jarvis" - don't know why but suspect some bluff old Naval Historian badgered us about it when we were at the Naval College. In any case there's plenty of locals who use "Jervis" and plenty who use "Jarvis". Seems there's lots of unusual pronunciations that vary between the English (as in British) use and the Australia use. e.g. Launceston iin Australian is Laun-ces-ton - makes sence to me! But in the UK it's Launs-ton! Lazy Poms!
As for Kosciusko - it's spelling was changed to the propoer Polish Kosciuszko in the late '90s to reflect the proper pronunciation...
As for Jervis Bay... I'll stick with the way the old Admiral wanted his name pronounced.
But either way, it's a top spot for a bit of camping!