I would say a permit is required if you ever plan to sell it.
You can always call it a 2 bedroom with an extra sleeping area.
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You can call it anything you want. Legality only would come into play if you were selling it and the newly constructed room does not meet the requirements for a bed room (at least 70 sq ft and an egress window, you dont even need a closet)
How one uses the property would be up to them. Many properties use their living room, dining room and or porches as bed rooms and advertise them as such.
Remember the type of space, size of space and the rent will dictate the type of tenants you get. Families - students - professionals all of which can have their own issues to you as a landlord and your neighbors.
As to whether it is legal - if you want to do it properly, you would have to call the Brookline Assessors Department to come in to reassess the unit in its new condition (3br/2ba) as opposed to a 2br/2ba. This would likely result in higher taxes. However, your unit would be stated to be a 3br/2ba at the Town Hall.
To be 100% sure, talk to an Attorney. They will be able to give you more accurate answers about the legality.