You can use the below command
$ aws s3 ls $BUCKET --recursive | sort | tail -n 1 | awk '{print $4}' some/other/object
Command explained
$ aws s3 ls $BUCKET --recursive -- Lists all the objects in bucket
$ aws s3 ls $BUCKET --recursive | sort -- Lists all the objects based on date
$ aws s3 ls $BUCKET --recursive | sort | tail -n 1 -- Selects the last line of the output ie most recent object
$ aws s3 ls $BUCKET --recursive | sort | tail -n 1 | awk '{print $4}' -- prints the name of most recent object