A vote is due to take place on what the new name of the Assembly in Cardiff Bay should be changed to.
It is understood the Welsh Government will back a move, tabled by the former first minister Carwyn Jones, to make the name for the national assembly bilingual.
Language campaigners have criticised the move, calling it "dishonest" ahead of the vote.
Earlier this year, the Assembly Commission introduced the Senedd and Elections (Wales) Bill, which also promises to give 16 and 17 year olds the chance to vote for the first time in the Assembly elections.
At the time, the Llywydd Elin Jones AM said, “The provision to lower the voting age to 16 will, I hope, engage young people in particular in the democratic process. The proposal to change the Assembly’s name to Senedd will better reflect the institution’s status as a parliament.
“After twenty years, this is a golden opportunity to renew our democracy and ensure that Wales’s national parliament enables us to do our best for our constituents today and for future generations.”
Plaid Cymru have also appealed to the First Minister to allow a free vote on naming the National Assembly for Wales and say it supports "Senedd" becoming the official name in both the main languages.
Mr ap Iorwerth said that whilst the matter went "beyond party lines", it was time to "take ownership" of one name that "belongs to each and every one of us".
Mr ap Iorwerth AM, Plaid Cymru deputy leadersaid, “Let's instead be confident in ourselves, uniting the nation behind the name that belongs to everyone regardless of their language, reflecting both our heritage and the dawn of a new kind of democracy. This is our Senedd, a unique name for a unique Parliament."