Select query to retrieve rows with null values
This example retrieves only "name" and the "SUM(credit)", when the
  "credit" has values.


The query you presented will retrieve a row for every present name, even if all associated credit columns are NULL. You get a row with a NULL value for SUM(credit) then. Null values are just ignored by the aggregate function sum():

You only get no row for a particular name if no row for that name exists in the table expenses for the given WHERE expressions.

I am assuming you want
.. only names matching 'vendor0%'
.. but all of those, even if they have no expenses in 2013.

Your query could work like this:

SELECT name, SUM(CASE WHEN date LIKE '2013%' THEN credit END) AS credit
FROM   expenses
WHERE  name LIKE 'vendor0%'
GROUP  BY name
ORDER  BY name


CASE defaults to NULL if no ELSE branch is given.
Aside: You shouldn't store date / time values as text. Use an appropriate type, it has many advantages.
And don't use "name" or "date" as identifiers. "name" is not a descriptive name and "date" is a reserved word in standard SQL and a function and base type name in Postgres.