i assume the following code is what you are expecting
update TABLE A
set A.COL = 6794
where A.id IN
(select id from TABLE B
where B.NAME = 'ABC'
and date(B.STARTDATE) = date (getdate())
)
And if you are sure that the ID column is having unique values, then you can replace the operator 'IN' with '=' in my code, otherwise use the code as it is