Below is for BigQuery Standard SQL
If you expect to get array you can use below
#standardSQL
SELECT ARRAY(SELECT name FROM UNNEST(children)) AS names
FROM `yourproject.yourdataset.yourtable`
you can test / play with it using dummy data as
#standardSQL
WITH `yourproject.yourdataset.yourtable` AS (
SELECT [STRUCT<name STRING, gender STRING, age INT64>('abc1','m',12),('xyz1','m',13),('uvw1','f',14)] children UNION ALL
SELECT [STRUCT<name STRING, gender STRING, age INT64>('abc2','f',12),('xyz2','m',13),('uvw2','f',14)]
)
SELECT ARRAY(SELECT name FROM UNNEST(children)) AS names
FROM `yourproject.yourdataset.yourtable`
output is
Row names
1 abc1
xyz1
uvw1
2 abc2
xyz2
uvw2
In case if you would expected string
#standardSQL
SELECT (SELECT STRING_AGG(name) FROM UNNEST(children)) AS names
FROM `yourproject.yourdataset.yourtable`
You can test / play with it using same dummy data
#standardSQL
WITH `yourproject.yourdataset.yourtable` AS (
SELECT [STRUCT<name STRING, gender STRING, age INT64>('abc1','m',12),('xyz1','m',13),('uvw1','f',14)] children UNION ALL
SELECT [STRUCT<name STRING, gender STRING, age INT64>('abc2','f',12),('xyz2','m',13),('uvw2','f',14)]
)
SELECT (SELECT STRING_AGG(name) FROM UNNEST(children)) AS names
FROM `yourproject.yourdataset.yourtable`
and output now is
Row names
1 abc1,xyz1,uvw1
2 abc2,xyz2,uvw2