SQL search multiple values in same field

Yes, you can use SQL IN operator to search multiple absolute values:

SELECT name FROM products WHERE name IN ( 'Value1', 'Value2', ... );

If you want to use LIKE you will need to use OR instead:

SELECT name FROM products WHERE name LIKE '%Value1' OR name LIKE '%Value2';

Using AND (as you tried) requires ALL conditions to be true, using OR requires at least one to be true.