AMs have backed renaming the assembly, calling it both Senedd Cymru and Welsh Parliament, in a vote on Wednesday.
A majority of AMs rejected the Welsh-only name Senedd and backed former first-minister Carwyn Jones’ proposals for a bilingual name.
But proposals to call AMs Members of Senedd Cymru or Member of Welsh Parliament were both rejected – the former by a knife edge.
A total of 43 AMs backed Mr Jones’ plan, versus 13 against.
Members of the assembly rejected a vote calling for the name to be purely Senedd, backed by Plaid Cymru and some Labour members, 16 for, 38 against, and one abstention.
The assembly is debating the Senedd and Elections bill, which also makes changes to how the assembly is elected and who can stand for it.
The votes are not the final stage in the matter, but are a major part of the process to decide what the final name will be.
Former first minister Carwyn Jones’s proposal for a bilingual name had sparked debate – supporters of the name Senedd have included BBC News presenter Huw Edwards.