##05AB1E, 51 42 41 bytes##
05AB1E, 51 42 41 bytes
2ô¦`ï<•r–ºþ¯Bê€õaPù£—^5AºüLwÇ–è•35B3ôsèsJ
Explanation
# implicit input, 123405
2ô # split input into pieces of 2, ['12','34','05']
¦` # push last 2 elements to stack, '05', '34'
ï< # convert month to its int index, 4
•r–ºþ¯Bê€õaPù£—^5AºüLwÇ–è•35B # get compressed string containing 3-letter months,
JANFEBMARAPRMAYJUNJULAUGSEPOCTNOVDEC
3ô # split into pieces of 3
['JAN', 'FEB', 'MAR', 'APR', 'MAY', 'JUN', 'JUL', 'AUG', 'SEP', 'OCT', 'NOV', 'DEC']
sè # get month at index retrieved earlier, MAY
sJ # join with 2-digit year and implicitly print, MAY34
9 bytes saved thanks to string compression, courtesy of @Adnan