They say a good boat name is one that you can Shout Out Loud! And a man can never go wrong by naming his boat after a special woman in his life.
The best storage yards in the Virgin Islands (in my opinion) include the yacht harbor at Virgin Gorda, Nanny Cay on Tortola and Independent Boat Yard on St Thomas. Nanny Cay is a good place to have things done in your absence and Independent Boat Yard is best for DIY work, who also offer reduced rates if you hire their yard personnel to simply prep & paint your bottom. Virgin Gorda offers the best long term storage rates but they are remote, their chandlery is very limited and supplies a bit more expensive.
Overall - I believe St Thomas is the better option simply because it's the most accessable, chandlery prices are better, provisioning options cannot be beat, fuel prices are way cheaper than the BVI and it's really the same cruising destination... St John & Tortola are less than a mile apart from each other!
But if I were to take delivery of a new old boat in the Virgin Islands, again - I'd give her a quick shake-down in the BVI and then spend a couple months getting to know the boat while cruisnig Down Island, making a list of things that need to be done and lay her up in Chaguramus, Trinidad - where you'll find scores of haul-out facilities and talented experts at a fraction of the cost of anywhere else in the Caribbean. The distance from St Thomas to Trinidad is only about 500 miles and there are hundreds of beautiful places to enjoy along the way. Trinidad is south of the hurricane belt so you can relax while you're away... and then come back and sail Up Island the next season and spend more time in your favorite spots enroute back to the Virgin Islands... assuming that's where you want to base your new boat.
That's how I'd do it... anyway.