Try putting another "current_day = day_names[day]" (no "var" needed) after line 18, so current_day updates when day does. However, that will cause problems since there are more days in a month then you have day names in your array.
Ideally, you should add another variable just to reference the day name, start it at zero, and reset it to zero every seventh time you update day. Then set "current_day = day_names[day_name_ref]" after line 18.
day += 1
day_name_ref += 1
if day_name_ref > 6:
day_name_ref = 0
current_day = day_names[day_name_ref]