Mr Davies said it was time to change the name in recognition of the primary law making powers it was granted in a 2011 referendum.
The Welsh word used for the assembly building is Senedd, which translates into English as "parliament".
But the Wales Office indicated that the move was "not a priority".
A spokesman for the Wales Office said any change in the name of the National Assembly would require changes to primary legislation.
Mr Davies, leader of the Conservative group in the National Assembly, the second largest party to Labour, describes himself as a "proud unionist".
He said his suggestion had nothing to do with any greater separation between Wales and the rest of the UK.
He said the move, which he claims would require only a small amendment in existing legislation to be in place by 2016, would be "a statement about the institution which now legislates for our great nation".
Mr Davies, the South Wales Central AM, said: "By voting for full law-making powers last year the people of Wales made their National Assembly a parliament in all but name.
"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.
"It would provide far greater clarity over the distinction between the assembly - as it is currently named - and the Welsh government, and it would give our devolved institution its rightful place alongside other national legislatures.
"As we drive forward it is crucially important that we embrace what we now have. Put simply - a parliament."
ANALYSIS by Adrian Browne, BBC Wales political reporter
Andrew RT Davies' suggestion that the National Assembly should be rebranded as the Welsh Parliament would appear to be aimed at attracting Plaid Cymru voters who might, he hopes, be uneasy about the leadership of Leanne Wood, who is up front about her socialist and republican beliefs.
It could also be seen as an attempt to assert his authority within his party.
There has been something of a whispering campaign about his leadership of the Tory group in Cardiff Bay for many months, and every leader needs to show who is in charge.
Although he is sometimes described as the Welsh Conservative leader, he's not.
David Cameron is the official leader of the party both in Wales and the UK.
There are those who will see this as Mr Davies engaging in a turf war with the Welsh Secretary Cheryl Gillan, over who calls the shots.
This theory is bolstered by the revelation that Mrs Gillan wasn't given advance warning about his call for a Welsh 'Parliament'.
This week he also told the Face to Face programme on ITV Wales that he would not have cancelled the Welsh Conservative conference last February had it been up to him.
Although he defended the decision in public, he said he fought the decision but was outvoted by the party's Welsh board.
This particular space in Welsh politics will be worth watching closely over the next few months.
He added that no expensive rebrand, new building or more politicians were required, but the name change would be simple recognition of the maturity of the devolution process.
"Some may say this is just a name change. I say there is a lot in a name," Mr Davies said.
The National Assembly was established in 1999, but until 2007 could not pass any primary legislation.
Between 2007 and 2011 it had to seek powers to pass laws from Westminster on a piecemeal basis, a process described by many as slow and cumbersome.
Since May 2011, it has been able to pass legislation in 20 devolved fields such as health, education and agriculture without reference to Westminster.
Asked whether he had discussed his call with the Secretary of State for Wales Cheryl Gillan, Mr Davies would only say that the pair "held discussions all the time".
A Welsh Government spokesman said: "This is a very interesting idea and certainly deserves further consideration. However, we do need to know the views of the Secretary of State for Wales on this matter."
Meanwhile, the Assembly's Presiding Officer Rosemary Butler said: "Terminology is important and there were undoubtedly difficulties in the early years of devolution in distinguishing in the public's mind between the National Assembly for Wales and the Welsh Assembly Government.
"Unfortunately changing its name is not something that is within the assembly's gift. It could be done only through legislation in Westminster.
"What matters to me is ensuring that the assembly continues to act as a fully-fledged parliamentary body, namely, by holding the Welsh government to account, making the best possible laws for Wales and representing Wales and its people."
A call for the National Assembly to be renamed the Welsh Parliament has been made by Conservative leader in the assembly Andrew RT Davies.