When Shaquille O'Neal took the court as a freshman for LSU, he was the first Shaquille to play in a major college sport, or professional sport. It was a unique name and would remain so for almost 2 decades.
Shaq's popularity apparently set off a baby boom of little Shaqs as fans across the country named their little ones Shaquille, or something similar (I looked for names starting with Shaq). I don't know how many little Shaq there were. The social security administration would likely have some idea. But approximately 20 years after O'Neal hit the spotlight, the little Shaqs had grown up and some of them joined the ranks of high level sports.
The second Shaq to play college basketball was Shaquille Johnson in 2009. Basketball-reference.com does not list birthdates or ages, but most likely he was born in 1991 or 1992, when O'Neal was at LSU or shortly after he was drafted by the Orlando Magic. Others quickly followed, and now there have been 24 Shaqs to play division I college ball. Most are in the 6'1 to 6'5 range. Giving a child the name of Shaq is a lot easier than giving him 7 feet of height. Two Shaqs stand at 6'9, and one, Shaquille Doorson, is 6'11 and 275 pounds. As of yet, the NBA has not seen a second Shaq.
The parents here may be naming their kid after a basketball player, but for those good enough to play college athletics there are a lot more spots open in college football than basketball. 43 Shaqs have played college football, with the earliest being Shaq Belson in 2008, a freshman year conveniently 18 years after O'Neal's. Eight of these Shaqs have gone on to play in the NFL, with heights ranging from 5'11 to 6'6. All were born between 1991 and 1994.
One of these Shaqs, Shaq Thompson, also briefly played minor league baseball. He is the only Shaq to play baseball professionally, but not successfully. He played the Gulf Coast rookie league, about the lowest level of the minors, and went 0 for 39 with 37 strikeouts. To the best of my knowledge, that is the worst batting line ever. Even the worst hitting pitchers, players selected for the sport independent of their batting ability, do better. Shaq quickly gave it up and has had success in the NFL.
No Shaq has played professional Hockey to date.
These Shaqs were born while O'Neal was playing for LSU, his early career in Orlando, and his first few years in LA. I don't know how many babies were named after Shaq while he won championships for the Lakers, but they would just be in high school right now. I suspect we'll see a good number more Shaqs in college sports in the future.
The big Shaq himself has sons named Shaquir and Shareef, but no Shaquille Jr. Shareef, currently in high school and standing 6'8, is a good enough basketball player to bring some attention to himself.