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."
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.