1] The evaluation of your formula in B3 :
=TEXT(DAY(A3),"ddd")
>>
=TEXT(DAY(Monday, October 01, 2018),"ddd")
The DAY function return integer from 1 to 31 (respenting the day of the month)
become >>
=TEXT(1,"ddd")
>>
Excel uses the 1900 date system, which means the first date is January 1, 1900
become >>
=TEXT(January 01, 1900,"ddd")
The formula result return >>
=SUN
p.s. However the result "Sun" is related to 1/1/1900 and don't related to 10/1/2018
2] The correct formula in your example is,
in B2 copied down :
=TEXT(A2,"ddd")
Regards
Bosco