Final answer:
The GDPR requirement allowing individuals to request the cessation of data dissemination or processing is 'the right to be forgotten'.
Step-by-step explanation:
Under the General Data Protection Regulation (GDPR), the requirement for processing personal information that states that individuals may request that their data no longer be disseminated or processed is known as the right to be forgotten. This right ensures that an individual can have their personal data deleted if there is no legitimate reason for a company to continue processing it. The GDPR applies to all member countries of the European Union and aims to provide comprehensive protection to individuals by regulating the collection and processing of personal data by both private businesses and government agencies.