If you have multiple string values you want to add, you can put them into a temporary table and then cross join it with the value you want.
-- Create temp table
CREATE TEMPORARY TABLE NewStrings (
NewString VARCHAR(50)
);
-- Populate temp table
INSERT INTO NewStrings (NewString) VALUES ('Hello'), ('World'), ('Hi');
-- Insert desired rows into permanent table
INSERT INTO PermanentTable (OtherID, NewString)
WITH OtherSelect AS (
SELECT OtherID AS OtherID FROM OtherTable WHERE OtherName = 'Other Name'
)
SELECT os.OtherID, ns.NewString
FROM OtherSelect os, NewStrings ns;
This way, you only have to define the strings in one place, and you only have to do the query in one place. If you used subqueries like I initially did and like Elendurwen and John suggest, you have to type the subquery into every row. But using temporary tables and a CTE in this way, you can write the query only once.