Create a custom formula field and make sure the return type is String. Then, write this formula:
If(Month(${Contacts.Date of Birth})==1,'01',If(Month(${Contacts.Date of Birth})==2,'02',If(Month(${Contacts.Date of Birth})==3,'03',If(Month(${Contacts.Date of Birth})==4,'04',If(Month(${Contacts.Date of Birth})==5,'05',If(Month(${Contacts.Date of Birth})==6,'06',If(Month(${Contacts.Date of Birth})==7,'07',If(Month(${Contacts.Date of Birth})==8,'08',If(Month(${Contacts.Date of Birth})==9,'09',If(Month(${Contacts.Date of Birth})==10,'10',If(Month(${Contacts.Date of Birth})==11,'11',If(Month(${Contacts.Date of Birth})==12,'12',''))))))))))))
This is more preferred than the name of the respective months' names because you will be able to arrange the groupings in reporting/dashboard.
You can also use this for any date field for that matter. Just replace the name of the field in the formula above to the name of your field.
Good luck!