you should be able to get insurance under your own name, but i'm not positive, doesnt hurt to ask. I'm sure you arent the only person in that situation.
as far as the engine or any mods to the car, the insurnace company is to be left under the impression its stock, no need to explain a 350. My iroc had that 383 with a 5 speed, was insured as a 305 tbi auto, lol, i've had cars insured that i drove only 3 or 4 times and the insurance agent never even saw. Ive had up to 3 cars on my policy and i'm the only driver, the 2nd and 3rd cars were like 200 bucks each a year for basic coverage.
when i got my 01 ss in aug '01, my insurance was 4,500 a year full coverage, collision, fire, theft, etc. i almost dropped but what could i do, now 3 years have passed and i'm down to 2500 for full coverage. However, this coming december i will be paying off the SS and dropping coverage to basic liability (i dont believe in collision insurance, long story) and before my insurance renews, i will turn 25, so my SS will cost me like 400 or less for the year.