This is my name. It always annoys me when people say "it sounds too much like Anesthesia" it actually doesn't they're pronounced differently. Anesthesia is pronounced like 'Ah-nehs-thee-zhya' (Ânêsthēžya) and Anastasia is pronounced like 'Ah-nah-stay-see-ya' (Ônôstêysēyû), so it is incorrect.
Some of the pronunciations include Ah-nuh-STAY-zhuh, Ah-nuh-STAY-see-a. Ah-nuh-STAY-sha, Ah-nuh-stah-SEE-yah, Ah-nuh-STAH-see-yah, Ah-nuh-STAS-yah. My favorites are: Ah-nuh-STAY-zhuh (English), Ah-nuh-stah-SEE-yah (Russian), and Ah-nuh-STAH-see-yah (European). And this is usually how my name is pronounced. I love all three pronunciations. :)