It was a predicament faced by Chris Cairns. It was also something Glyn Meads had to deal with. And Martin and John Leslie.
Some live up to or exceed expectations, others toil away while yet more become fed up with the attention and choose to slip quietly into the relative obscurity of everyday life. Don Bradman's son John went as far as to change his name by deed poll to Bradson to escape the comparisons.
You might not have heard of Jarrod Smith but you've probably heard of his dad Ian. That's Ian David Stockley Smith, the former New Zealand wicketkeeper who played 63 tests and 98 one-day internationals between 1980 and 1992 and who was New Zealand Player of the Year in 1989. It's also Ian Smith the TV cricket commentator.
It's with reluctance that Jarrod talks about his dad. It's not that he's ashamed or doesn't get on with his father, it's just a sticking point.
"It's part of the reason I wanted to go to America because no one knows who he is over there," Smith said just hours after arriving in the country from his base in the US. "Any success I have is Jarrod Smith, not Jarrod Smith son of Ian. It's no disrespect to him because I'm very proud of what he's done.
"With cricket it was always a bigger problem. I played a lot in my younger years and there was pressure to succeed. Football wasn't so bad because the name wasn't so important."
The 21-year-old played age-group cricket for Central Districts but gave the game away when selected for the NZ Schoolboys football team, realising he couldn't do justice to both sports.
"I always enjoyed football more, still do, and have no regrets about my decision," he explained. "I think my dad always knew I was more likely to do well in football than cricket. Maybe because of his name, maybe not. He didn't try to push me into cricket, he just wanted me to be happy."
Of course cricket's loss is football's gain and Smith gets a chance to make a name for himself when he takes on Malaysia.
He might not see any action in Christchurch today, with coach Ricki Herbert putting out his best side, but he is likely to take to the playing field at North Harbour Stadium on Thursday night in the company of his dad.
As a relative unknown on the football scene, largely because he's spent the past three years at the University of West Virginia, Smith falls into the category of player that Herbert describes as "potential".
The All Whites boss wants to use 2006 as a chance to cast his eye over a number of players who could become integral to his plans for the 'Road to South Africa' and the 2010 World Cup.
"This is a little bit of a voyage of discovery for us and, while we had him in the Olympic campaign in 2004, it will be another step up for him," Herbert explained. "He's athletic, he has got a physical presence and he's generating favourable reports from the college system."
Smith has one year left on his scholarship at West Virginia, not known as a top football school, after which time he hopes to be drafted into the MLS in the US.
His tally of eight goals left him third-top goalscorer in the Big East conference but he is aiming for twice that when the new college season kicks off in August, something that should see him talked about among MLS talent scouts.
"The perfect scenario would be to have a couple of good years there and then make my way into Europe," Smith casually explained. "I'll be doing all I can to get into that draft for the MLS."
Making a name in the MLS is becoming an increasingly popular route for aspiring New Zealand footballers and certainly served Ryan Nelsen and Simon Elliott well.
Firstly, however, Smith wants to make a name for himself in New Zealand this week and, while he admits it will more often than not be accompanied by a mention of his father, it's the start of the process of becoming Jarrod Smith the footballer.
- HERALD ON SUNDAY
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