This should be name of the 'home' organisation of the person who is submitting this notification to UKRI. This does not need to be the same as the organisation that held the award that the publication is acknowledging.
If you are an author who is notifying UKRI of an exemption that you have applied to your publication and you are not currently associated with a research organisation, then you may either write n/a or include here the name of the organisation where you held the funding that the output is acknowledging.