Her birthday is unknown since she was in an insane asylum when she was changed and does not remember anything about her human life. Her full name is Mary Alice Brandon Cullen (New Moon page 400).
From Alice: Full name: Mary Alice Brandon Cullen तारीख, दिनांक of Birth: Some तारीख, दिनांक in 1901(not absolutely sure) From Ashley: Full name: Ashley Greene तारीख, दिनांक of birth: 21 February 1987, Jacksonville, Florida, USA
Noone knows when her birthday is. It states in New Moon that she couldn't find the file या whatever that has her Birthday on it. All we know is that she was born in (1901). Her real name is Mary-Alice-Brandon