Why are the letters U, V and W used in AC motors to represent the windings?
The letters are "representative of something"

To assist in providing an international standard the International Electrotechnical Commission (IEC) created that IEC 60034-8 standard. 
"Terminal markings and direction of rotation"

An electrical machine compliant to 60034-8 will ensure that clockwise rotation of the drive shaft will occur for positive electrical phase sequence U-V-W.

Thus if you were to wire such a machine upto a distribution labeled A-B-C and these electrical phases were A leading B, leading C... you would have the expected mechanical rotation

is it "just another set of letters"? you could say they arbitrarily chose that sequence, a sequence that is just as good as any other BUT they assigned a specific meaning to it and a meaning that is internationally recognised. 

MotorA from supplier A and MotorB from supplier B being compliant to this reg &amp; meeting the customer requirements would be drop-in replacements that would minimise any unexpected mechanical rotation