Taoiseach Leo Varadkar says they may look at introducing a proviso that the government will have to be consulted on name changes for stadiums when they are providing grant assistance for new or redeveloped grounds.
Mr Varadkar was speaking in Galway on his way in to watch Connacht against Bristol Bears in the Champions Cup on Friday night at a venue which had until that morning been known as the Sportsground for 97 years but had changed overnight to Dexcom Stadium.
He said there was a big difference between changing the name of a venue like the Sportsground to one which had been named in honour of an individual, such as nearby GAA ground Pearse Stadium, which commemorated 1916 patriot Pádraig Pearse, or Páirc Uí Chaoimh in Cork which honoured a man who had given decades of service to the GAA.
"I think it depends on the circumstances," said Mr Varadkar. "Páirc Uí Chaoimh was named after a person, an individual who contributed to the GAA enormously for decades.
"The Sportsground is different, it's not named after a person, so I do think circumstances are different.
"Broadly speaking to people in Galway and rugby fans for Connacht, they are delighted that Dexcom is investing in this ground, besides the €20 million the government is putting in, building something that the city deserves and the region deserves and needs, which is a high quality stadium."
Tánaiste Micheál Martin pointed out this week when heavily criticising the proposed name change to Páirc Uí Chaoimh that the government did not seek naming rights or impose conditions when they poured millions of euro into the project.

The government are contributing €20m to the redevelopment of the Sportsground in Galway, which is half of the total cost of €40m. That will see the permanent capacity increase from 6,000 to 10,000, along with the construction of a high performance centre and other developments.
Connacht’s home will be named Dexcom Stadium for the next 12 years after the US multinational, which manufactures glucose monitor devices which help manage diabetes and which is about to create 1,000 jobs when it opens its first European manufacturing site in Athenry in a €300m investment, secured the naming rights to the city centre venue.
Mr Varadkar said they can’t retrospectively impose conditions on grants already issued but he said they were looking at making changes to future applications.
"One of the things we are considering doing for future grants, it can’t be done retrospectively, is if we are putting a lot of money into a stadium or into a university building, for example, we could put it into the grant of permission that it would require government to be consulted on naming.
"But that would only apply to future grants, not existing ones," he added.