Best eaten immediately. Leftovers keep 2 days but the shrimp firm up — warm gently in a pan with a splash of water, never the microwave. Don't freeze.
Frozen is usually better unless you live by the coast — most 'fresh' shrimp at the counter was previously frozen anyway. Thaw under cold running water in about 10 minutes.
The butter split. Keep the heat moderate and add pasta water gradually while tossing — the starch holds the emulsion together.
In Italy scampi are langoustines. The garlic-butter-lemon preparation became known as 'shrimp scampi' in Italian-American cooking — literally 'shrimp langoustine' — and the name stuck.