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.