They can run reign years and Anno Domine years in parallel. That is historical; the church kept track of the latter with most others using the former.
In game terms, the latter gives us an easy to use timeline, with the former providing character.
They could also drop the numbering of rulers of the same name from routine use; at most people would refer to "old king Edward" or use their nickname to distinguish them from a same-name successor. It's always been slightly jarring to have the numbers used throughout the game. It's fine to have it on the Chronicle or the reign list, though.
In game terms, the latter gives us an easy to use timeline, with the former providing character.
They could also drop the numbering of rulers of the same name from routine use; at most people would refer to "old king Edward" or use their nickname to distinguish them from a same-name successor. It's always been slightly jarring to have the numbers used throughout the game. It's fine to have it on the Chronicle or the reign list, though.