Generation Y began in 1977-1982. It is not black and white, it is a shaded gray area. Some people in this time frame will identify with Generation X while others may identify with Generation Y. It mostly depends on their parents, friends, and childhood upbringing.
The peak of Generation Y was from 1982-1993. Nearly all of the people born in this range are true echo boomers.
From 1993-2001, Generation Y trails off and starts fading into Generation Z the same way Generation X faded into Generation Y from 1977-1982. It is an exponential slope, so those born closer to 1993 (until 1995 or so) will be more likely to identify with Generation Y. From 1995-2001, if they were the younger siblings of a true echo boomer they may be more inclined to declare themselves from Generation Y, while some who have Generation X parents and/or without older brothers and sister may identify more with Generation Z.