I have a log with records. How do you call a person who adds records to this log? a Logger maybe?
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,
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.
A word used in business is loggist. Although I can't find it in any dictionaries, it can be found in job descriptions such as this one:
The Civil Contingencies Act (2004) establishes a clear set of roles and responsibilities for those involved in responding to and recovering from an emergency.
Our training is for those people who have been given the role and responsibility for keeping records and logs during emergencies and crises.
We help learners to gain the knowledge, understanding, skills and confidence required for the loggist role by using good quality teaching with structured group activities and exercises.