During my time in the US Army I prepared the "Morning Reports" for 4 companies, making up my battalion.
It covered names, ranks, status, location to account for everybody.
It tied into what is/was called the TO & E, which is the authorized strength by headcount, rank, and equipment of a unit.
I am sure it is far more automated than when I did it. I do remember if an individual went AWOL, my report was the official document recording his status change, for the official record.
We did NOT hold muster each morning to count heads. Squad leaders, company commanders and company clerks would phone reports to me, to prepare the reports. I would dial Heidelberg and give a verbal summary over a secure field phone line, and later prepare computer versions as well.