That's quite a story to follow, especially in such a football-obsessed country, but Simeone is coping so far.
"It's not a burden but a challenge to have this name," Simeone told the Argentine newspaper Ole. "I know a lot of things give me a plus. I am proud that my dad is someone so important in football and the national team. He is an example for me but I haven't [made it] here because I'm the son of [someone famous]."
Such a background brings both opportunities and pressure, and players often have to work twice as hard to prove they are not riding on coat-tails.
"Some people thought that he was here just because his name was Simeone," teammate Emanuel Mammana told Ole. "But he winds up being a humble guy and a great teammate. The truth is that he kills himself in practice in order to be a great forward."
Simeone has been at River Plate since 2008, and the 19-year-old has made 27 appearances for the iconic Buenos Aires club in the last two seasons. But it was his performances at the South American Under-20 Championships this year that set tongues wagging. Simeone scored nine goals to top the charts (the next best was five) and briefly threatened the all-time record of 11. Argentina beat the big guns, including Brazil, to take the championship and confirm their favourites tag for this World Cup.
There will also be plenty of expectation from home. Argentina have won this event six times - more than Brazil, Germany, Italy or any other nation. It started with the Diego Maradona-inspired title in 1979 and more glory followed in 1995, 1997, 2001, 2005 and 2007. The Albiceleste have also produced some of the biggest names of previous tournaments, from Maradona to Javier Saviola, Sergio Aguero to Lionel Messi. Could Simeone be next?
Argentina are in action on Saturday, facing Panama in Wellington (4pm). They then play Ghana - in what could be one of the games of the tournament - next Tuesday (7pm) before their final group match (versus Austria) in the capital on Friday, June 5.
Giovanni Simeone
Age: 19
Height: 1.75m
Club: River Plate (Argentina)
U-20 caps: 9
U-20 goals: 9.