If col1 is indexed, it would be best (performance-wise) to split the query in two:
SELECT *
FROM mytable
WHERE col1 = name
UNION ALL
SELECT *
FROM mytable
WHERE name IS NULL AND col1 IS NULL
This way, Oracle can optimize both queries independently, so the first or second part won't be actually executed depending on the name passed being NULL or not.
Oracle, though, does not index NULL values of fields, so searching for a NULL value will always result in a full table scan.
If your table is large, holds few NULL values and you search for them frequently, you can create a function-based index:
CREATE INDEX ix_mytable_col1__null ON mytable (CASE WHEN col1 IS NULL THEN 1 END)
and use it in a query:
SELECT *
FROM mytable
WHERE col1 = name
UNION ALL
SELECT *
FROM mytable
WHERE CASE WHEN col1 IS NULL THEN 1 END = CASE WHEN name IS NULL THEN 1 END