I wish to become . . . . . . . . eye surgeon.

Answer: Option B

'An/A' is used as an indefinite article for a thing or person when the reader doesn't know which one we are referring to out of many nouns. It states the random nature of the subject.
Option B is correct because 'An' is used with a word 'Eye' having a vowel sound to indicate a single countable noun which is random in nature.