So who decided on the name then?

It's been argued that the Assembly's House Committee decided on the name Senedd last June. Well here's the relevant minute:

New Building Update HC(2)-06-05(p3)

The Deputy Clerk presented House Committee with an update on current progress and issues relating to the construction, fit-out and operational policies of the New Assembly Building. Members noted or agreed the following :
* a site visit to view the building had been arranged for Wednesday, 6th July. Members would decide access arrangements following the visit;
* the names allocated to spaces in the Senedd, which would be used in future;
* final completion of the works under the building contract was scheduled for 30th August. However, some slippage in aspects of the building works would cause delay in the start of the fitting out programme. The slippage had been caused by a combination of factors including changes to ICT requirements and late delivery of equipment to site;
* options for child care facilities in the Bay were being considered and a questionnaire would be issued shortly;
* a Member asked that assurances be given by the contractor that the New Building complied with building regulations in respect of the first floor service access, which could only be accessed via a lift;
* in addition to the link access, external access for Members should also be considered through a convenient door in the Assembly Offices;
* the desirability of fire doors being open but with automatic closing devices in the event of fire. The House Committee agreed to accept the recommendations of the paper apart from the issue of access, which would be resolved after the site visit on 6th July.

The building is therefore referred to as 'New Building' and 'New Assembly Building'. Something called Senedd is mentioned, but nowhere defined. So make of that what you will.