The Social Enterprise Coalition changed its name to Social Enterprise UK earlier this month.
The WSEC and Senscot, the network for Scottish social entrepreneurs, both questioned at the time the implication that Social Enterprise UK represented the whole of the UK.
Now John Bennett, chief executive of WSEC, has told Third Sector there had not been enough consultation on the change and his organisation had received a number of communications expressing concern about the rebranding.
"Social Enterprise UK does not have the power to represent the views of social enterprises in Wales to the Welsh Government," he said.
"I feel there is an urgent need to determine what the relationship will be between Social Enterprise UK and Wales, and indeed other organisations, to ensure that there is a coordinated voice in the United Kingdom that can influence policy in Westminster."
He said it would make sense for Social Enterprise UK to be called Social Enterprise England.
Celia Richardson, director of communications and policy at Social Enterprise UK, said it had consulted Bennett about the name change prior to the rebrand, and had been under the impression he had no problem with it.
She said the organisation had no plans to change its name again but it would be happy to meet with the WSEC to discuss the issue.