It's pretty hard to give a proper answer without knowing the data set & the data type you have there. Attaching the workbook would help seeing clearer
However if your date field is a date type in Tableau (little calendar icon ) which contains all the date (past and future) of your data set. Then you can create a calculated field based on the date field that would look like that:
IF DATEDIFF('month',[Your Date field],TODAY())=0 then 'Current month'
else 'Other period'
Have a try with that first and see if it works
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