The cases of mistaken identity are easily understood. After all, both players wear trendy Under Armour attire, have swings to die for and are of similar ages. Paul Dunne has had a number of requests for autographs these past few days only for people to realise he is not Jordan Spieth. “When I put my head down, they just see the sign on my hat . . . and then they’re disappointed when I bring my head up,” he said.

Maybe they should take his autograph anyway, for the 22-year-old from Greystones has his own star appeal. A recent graduate in Business Finance from the University of Alabama, Dunne – a likely prospect for Walker Cup selection later this year – signed for an opening round 69, three-under-par, in the first round to make his own statement of intent.

The cut

A year ago, Dunne missed the cut on his Open debut at Hoylake. This time, more mature and less inclined to feel like a rabbit stuck in the headlights, he has felt very comfortable rubbing shoulders with the world’s best players. In practice, he had played with Graeme McDowell and Francesco Molinari and was encouraged by the compliments about his ball-striking.

“I think my game has progressed a little bit every year. I feel like it’s better this year than last year, which was better than the year before. If I can keep going, just improving every year, then I’m sure I can compete in a lot of tournaments around the world.”

And they don’t get any bigger than this one. So, the influence of having Alan Murray, a fellow-Greystones man and his coach out at UAB on his bag, was also a big help.

“It’s great,” says Dunne. “For four years, he’s seen me play every day. Every day we practice and play in tournaments, he sees us. He was at the European Boys’ (in Finland) last week and I called him and asked him would he caddy for me and he said, ‘absolutely’. He jumped at the opportunity. It’s great to have someone who knows your game that well on your bag.”

Dunne’s birdie-birdie start meant that, as he walked to the third tee, he could see from the digital leaderboard out on the course that, at that point, he was tied for the lead. “My first thought was, ‘Is anyone at home going to take a picture of it on the computer screen and send it to me later?’ . . . it’s kind of a novelty thing for when I’m 70 years old, sitting in a bar, having a pint, maybe telling someone that I led the Open.”

Such ideas of reminiscing are for far into the future, for Dunne is very much one to stay in the moment when on the golf course. His first round featured four birdies, all of which came on an outward 32, and just one bogey, on the 11th.

On the first, he hit a wedge approach to 10 feet for birdie; on the second, another wedge from an identical yardage to five feet, and on the fifth he got up and down from greenside rough. His fourth birdie was, as he put it, “a nice bonus.” In trying to two-putt from 90 feet, he rolled in the putt.

Toughest stretch

Coming in on the tough finishing stretch, Dunne two-putted from over 120 feet on the 15th for par, then got up-and-down for par saves on the 16th and the 17th. His play of the Road Hole demonstrated maturity. He hit a three-iron left and long, avoiding the deep bunker, and then pitched to inside a foot.

“It’s only one round of a four -round tournament event, so there’s a long way to go. I’m sure the weather will throw a lot at us and I can only try to keep hitting the targets and try to commit to the shots,” said Dunne.

The contrast with his upbeat mood and that of Shane Lowry was marked, as the latter – with heightened expectations after a top-10 finish in the US Open – fell victim to the par four 17th. Lowry had recovered well from a nervy start, which saw him two over through four holes.

He had five birdies in an eight-hole stretch from the seventh to the 14th to get to three-under only for the famed Road Hole to bite him. Lowry’s tee shot on the 17th finished out-of-bounds in the Old Course Hotel. His next tee shot – his third – found heavy rough. He went from rough to rough to rough in running up a quadruple bogey eight in signing for a 73, and – understandably – was in no mood for post-round chat.