In law exams do you have to use the full case name eg could 'Bolam v Friern Hospital Management' be shortened to 'Bolam'?

It depends what case it is. If its a short one like Nettleship v Weston, you should use the case name, but for some you could use the scenario to name it, e.g. the Wagon Mound case. For this case I put Bolam v Friern Barnet.