The leader of the Conservative party in the Welsh Assembly, Andrew Davies, has called for the devolved governing institution to be renamed the Welsh Parliament.
At present the Welsh have a National Assembly, reflecting the lesser degree of devolution than their Scottish counterparts, who have the Scottish Parliament.
The calls have come after a change in the law in 2011 which finally allowed the Welsh Assembly some limited law-making powers without the need to seek authority from Westminster. This, Mr Davies believes, is sufficiently significant a change for the Welsh Chamber to be renamed a Parliament.
The Welsh Assembly already enjoys parliament status in the native Welsh language, in which the term for the assembly building is 'senedd' which translates to 'parliament'.
Mr Davies went on to add that he was a unionist and that the call to change the name of the assembly was not linked to a desire to see greater devolution from Westminster.
Speaking about the proposals, Mr Davies said that the fact the assembly could now pass some laws made it a legislature.
"By voting for full law-making powers last year the people of Wales made their National Assembly a parliament in all but name," he told the BBC.
"It's now time to reward their faith in our institution and acknowledge that where laws are made, the title of a parliament should exist. This is a common-sense move," he added.
He added that the move to change the name would not be expensive, stating that no significant rebrand was required, nor was it necessary to appoint new staff.
The National Assembly for Wales was created by the Government of Wales Act 1998 under the then-Labour Government. In 2007 it acquired law-making powers under the Government of Wales Act 2006 but in order to pass legislation authority had to be granted from Westminster.
Since the 2011 referendum, the parliament has had the authority to pass laws in twenty areas including health, highways, education, social welfare, tourism and agriculture.
The change in the name cannot be completed without authority from Westminster and would therefore need the support of the Westminster Coalition Government and particularly the Secretary of State for Wales, Cheryl Gillian.