Businessman John Adams renamed Palleg golf club in Swansea the Celtic Minor to attract more members.
But a spokesman for Celtic Manor warned they will fight "any attempt to take unfair advantage of their reputation".
Celtic Minor said "there wasn't any issue" with the name change.
Club manager Melanie Eaton said the name change "works in their favour."
She added: "You put Celtic Manor into Google and there's the Celtic Minor popping up underneath it so there are advantages of having a similar name.
"The club had been established a long time and initially the members didn't want a name change. But the response we get from most of them is brilliant.
"The club was relatively run down when it was bought out and the new owner has spent a lot of money."
The Celtic Minor golf course is 53 miles (85 km) away from the Celtic Manor, which is owned by billionaire Sir Terry Matthews.
A Celtic Manor Resort spokesman said: "The Celtic Manor Resort would like to make it clear that Celtic Minor Golf Club has no affiliation with the Celtic Manor Resort or its three championship golf courses.
"Celtic Manor is a registered trade mark of Celtic Manor Resort Limited (UK) and we reserve all our rights to protect our name from any attempts to take unfair advantage of our reputation or to exploit our goodwill in these services."

Cracks in its structure were spotted in March and the area was sealed off.
The IFA has confirmed to the BBC that it received a preliminary engineer's report into the damage and is studying the findings.
The venue is scheduled to host the Euro 2016 qualifier against Romania on 13 June.
Kevin McShane of the Institute of Civil Engineers told BBC Radio Ulster's Good Morning Ulster programme that it was a surprise "nothing more serious" had happened because the foundations had moved.
"We can see at the base of the columns that the wall and the beams have moved," he said.
"That's caused stress throughout the structure, given the shape of the structure it's very top heavy, it's leaning on one side towards the pitch.
"So if there's some problems with the foundation, the natural reaction of the whole structure is to try to topple over onto the pitch."
On Wednesday, the IFA's chief executive Patrick Nelson said staging the international at Windsor Park remained its "only focus".
He said an alternative venue for the qualifier, such as the Kingspan Stadium, had not yet been considered.
It is believed that at least two independent reports are being carried out on the damaged stand, with cracks first spotted on 31 March, two days after Northern Ireland's Euro 2016 qualifier against Finland.
Linfield are unable to use their home venue and the Irish Cup final on 2 May, which was scheduled to be played at Windsor Park, has been switched to the Oval.
Bosses of the Celtic Manor, which hosted the Ryder Cup and the Nato summit, are threatening legal action against a village club changing its name to Celtic Minor.
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The Irish Football Association (IFA) has been advised to demolish the damaged west stand at Windsor Park, the BBC understands.