Vocabulary – What to Call a Person Who Adds Records to a Log

Depending on the field it can be specific,

I would avoid "logger", as it can mean "lumberjack", and when used in a business context usually refers to software that generates logs, not a person who creates them.

Data entry clerk

Is common if you're talking about a person who professionally enters data.

As with any written record you can use,

Author

or

Recorder

My preference would be "recorder" given that it is a term used to describe a person who takes down records, which seems best for your situation.