Why are a person's details entered next to the process name in the record of processing activities?

ANSWER

This is the person responsible for the given process — its owner. This is important from the perspective of shared responsibility for the content and currency of the register. Without information from the process owner, the person maintaining the register, e.g. the DPO, will not be able to keep it up to date.

This practice is encouraged by PUODO — Guidelines and explanations concerning the obligation under Article 30(1) and (2) GDPR (p. 9):

"In some cases it may be justified to additionally note in the register information such as: identification of so-called process owners, i.e. persons responsible at the controller for specific processing activities (e.g. the head of a given organisational unit, a dedicated post, etc.) (...)."