Month should be mention in payslip
There is a date on the form. And there are Description fields for every payslip item you enter where you can describe the item as being for a date range or month, if you wish.
The problem with this is that, period of payroll doesn’t only differ from county to country but now from company to company. Some companies do weekly payroll, other every 2 weeks, others every three month etc. So utilize custom fields, and with custom theme you can put the month anywhere you want on the payslip.