Categories Range of Date into MMM-YYYY

Use below formula in B3 and copy down.

Formula:

=IFERROR(IF((A3>=DATE(YEAR(A3),1,1))*(A3<=DATE(YEAR(A3),7,1)),TEXT(DATE(YEAR(A3),7,1),"mmm-yy"),TEXT(DATE(YEAR(A3),1,1),"mmm-yy")),A3)