One way:
data have;
input dob $;
datalines;
07/1980
03/1978
10/1982
;
data want;
set have;
dobnum = input(dob,anydtdte.);
format dobnum mmyys7.;
/*redundant*/
month = put(dobnum,monname. -L);
year = year(dobnum);
run;
The Input creates a date value using a very flexible approach for many date layouts. In this case it will assume that the day of the month is 1.
The Month and Year are redundant because you can get them easily from the Dobnum variable by applying a format if needed. The -L in the Put is the left justify the value so that there aren't any leading spaces in the month text.