If you want to reference this task type in lists, workflows, reports, then it could be as simple as a naming convention. Tasks can be filtered by Task title, so if you use for example “[Type] | [Contact first name] [Contact last name]” as your naming convention, reps would be able to filter all their nurture tasks by searching for “Nurture”, “Customer” etc.
If workflows are creating your tasks, you would need one if/then branch per value: One branch that creates tasks named “Nurture | [Contact first name] [Contact last name]” and so on.