As Anton has highlighted - this is an often asked question - with some very good research threads out there. The simple answer is - if the supervisor has not contributed in any meaningful way - then they do not have to be acknowledged. However, this can be fraught with issues - arguments, supervisors 'black-listing' your reputation etc. The only clear line of defence is to draw up an agreed formal contract at the beginning of any supervisory arrangement to clarify what the exact position and expectations are - for all parties concerned.
The supervisor's name is not absolutely necessary, however if some help has been taken from the supervisor during writing the manuscript, then this should be acknowledged.