I tested the scripts in one of dev box in SQL2016. the results are below. Each scripts ran 100 times (at 2 different times)
Included the method suggested by Scott Pletcher 

CONVERT(CHAR(2), SomeDate, 1)

Run#1
Method        AvgTime(ms)
PRECAST Method        553.07    
DATENAME Method        518.48    
MATH OVERRUN Method    526.75    
ScottPletcher Method    483.83    

Ru#2
PRECAST Method        565.5    
DATENAME Method        515.25    
MATH OVERRUN Method    526.97    
ScottPletcher Method    501.11