So surely now he's treated like a superstar in Mumbai. Not quite.
A laugh, then "maybe I'd be a little bit more well known if people could say my last name".
"I like sitting back, being in the shadows and letting all the big dogs get that kind of stuff. It's nice to be part of a team with so many big stars, who are followed so closely. In the city we're in, the fans are fanatical at times."
This IPL is, in addition to being an event in its own right, a preparation for the Champions Trophy, which starts in England at the end of this month.
McClenaghan is back in the New Zealand squad, not having been required last season, and having had a rotten run of injuries since the start of last year. Then, there's a spot of bowling reinvention that's gone on too. We'll come to that.
Last season, McClenaghan suffered a nasty eye injury against Pakistan in an ODI in Wellington, when a short ball got through his grill and fractured his eye socket.
It sidelined him for a couple of months. Then he was sidelined by a pelvic issue, and during the last New Zealand season broke a bone in his foot.
He got in three Plunket Shield first-class games at the end of the season, before returning to India.
He'll be playing his first ODI in about 17 months at the Champions Trophy, which is a shame considering his numbers in the 50-over format are outstanding. The IPL has been a massive learning ground for McClenaghan. He has improved to the point where he's one of the best-regarded fast-medium bowlers in the shortest form of the game.
"When I first came into the New Zealand team I was a good bowler in New Zealand and South African conditions, where there's a bit of bounce and pace in the wickets," he said.
"My first sub-continental tour was to Bangladesh and I got smashed. The surfaces were slower and I didn't have good change-ups [changes of pace], that's necessary in sub-continental conditions.
"I'm now a more well-rounded player and able to compete in all conditions against all types of batsmen. It has done me the world of good."
So what's the mindset like when a Virat Kohli, AB de Villiers or any of the other superstar batsmen in the IPL clatters into you?
The answer is to put it out of the mind swiftly and move forward.
"I've conceded a couple of big overs and it's how you come back from that and bowl a good next over, and not get flustered.
"You need versatility, first and foremost, being able to adapt your plans to batsmen and conditions. And you need a very short memory, and not get hung up if you've had a bad game and take that into the next one."
Talk to any overseas player about the big benefits of the IPL and high on the list will be the camaraderie that develops, the mixing with top players from other countries.
It's certainly removed much of the old national antagonism between players - perhaps other than India v Australia, which remains a fractious environment.
So McClenaghan is playing with Jos Buttler (England), Kieron Pollard (West Indies), Malinga and some of India's biggest names.
He talks of his captain, Indian batting star Rohit Sharma - owner of the highest ODI score, a barely believable 264 against Sri Lanka three years ago and who has two of the five double tons in one-day internationals - and his partner as good friends. Former Australian quick Mitchell Johnson, unable to get a look-in this campaign at least partly down to the New Zealander, has been great company and a top source of advice. "You rub shoulders with people who have been there, done that, they keep you calm in pressure situations. I'm loving it. Each year it's a new experience."
New Zealand coach Mike Hesson recently called McClenaghan "probably our best death bowler" and praised him as the most consistent in the back end of overs and offers an attacking option through the middle on flat surfaces."
Ah yes, the death phase.
As New Zealand were charging towards the World Cup final two years, ago, McClenaghan, who had been a key figure in the period before the tournament, found himself surplus to requirements in the cup, playing just one game. He didn't fit in the game plan. It hurt.
So he sat down with his mentor, former Auckland and New Zealand seamer Kerry Walmsley.
"We made a plan. I had to find a way to build a set of skills that are valuable to New Zealand cricket. What do we struggle with the most? It's bowling at the death."
That's the period in the final stages of an innings, when batsmen go hard, damn the consequences and bowling figures can go into orbit.
"We worked on that for a year and it kind of translated into success in T20 cricket, which boosted me back into contention for the one-day team.
"Now I really enjoy it, knowing and accepting that some days at the death you may get hit for 20 in an over because you miss, or a guy played a couple of good shots, or he gets lucky. Then you have days when you go for five an over."
McClenaghan, 30, says his body is in good shape, despite the relentless play/travel/play nature of the IPL. Whatever chance he has to get away from the cricket he takes.
Mumbai's game against Delhi Daredevils early tomorrow comes after a five-day break, easily their longest of the competition, which at one point had them play eight games in 17 days.
"I've been trying to manage the body, get sleep, still get gym work done. It's very demanding mentally and physically.
"I'm working hard to get in the best shape possible for the Champions Trophy. It's going to be a massive tournament and I'm feeling in a good spot."
New Zealand play Australia, England and Bangladesh in a narrow window from June 2, before semifinals and a final. It's a short, sharp, high calibre event, with no soft matches. Only the eight top-ranked nations take part.
"Every game you're going to have to be at 100 per cent. If you don't turn up you're going to get cleaned up because the other teams are too good.
"We'll go in with the mentality we've always had; prepare as well as you can and then hopefully performances take care of themselves."
By the numbers
ODI: 48 matches, 82 wickets at 28.2.
T20: 28 matches, 30 wickets at 25.26.
IPL: 36 matches, 50 wickets at 23.7.
Overall T20: 114 matches, 151 wickets at 22.03.
