Under the GDPR, they have the right to delete their name and other personal data from the database, not their content.
Some exceptions apply such as if they wrote their name or other personal details into their comment. Those parts would be covered by the GDRP but that’s indeed exceptional, not the norm.
The comments we write here are “only” protected by copyright.
How exactly that manifests? Who knows. It’s the same as IRC logs or mailing lists archives. A quick not at all exchaustive search revealed no relevant legal cases.