Just make two calls to SPLIT_PART, one for each desired column:
SELECT
SPLIT_PART(assoc_name, ',', 1) AS assoc_name,
SPLIT_PART(assoc_name, ',', 2) AS assoc_last_name
FROM mytable;
If you want to persist this view in a database table, then try using INSERT INTO ... SELECT, using the above select:
INSERT INTO someOtherTable (assoc_name, assoc_last_name)
SELECT
SPLIT_PART(assoc_name, ',', 1),
SPLIT_PART(assoc_name, ',', 2)
FROM mytable;
To handle the case where one/both of the above calls to SPLIT_PART might return NULL, and the target column be non nullable, then consider using COALESCE:
INSERT INTO someOtherTable (assoc_name, assoc_last_name)
SELECT
COALESCE(SPLIT_PART(assoc_name, ',', 1), ''),
COALESCE(SPLIT_PART(assoc_name, ',', 2), '')
FROM mytable;