Even LIKE can use an index in SQL. It depends on the wildcard.

Code
-- tested with MySQL 5.6

-- index is used for accessing entries starting with "ba"
EXPLAIN
SELECT * FROM history
  WHERE name LIKE 'ba%' LIMIT 10;

-- index is used for accessing entries starting with "b". Get entries ending with "r" by filtering the "b" results
EXPLAIN
SELECT * FROM history
  WHERE name LIKE 'b%r' LIMIT 10;

-- no index used
EXPLAIN
SELECT * FROM history
  WHERE name LIKE '%ar' LIMIT 10;
Result
idselect_typetablepartitionstypepossible_keyskeykey_lenrefrowsfilteredExtra
1SIMPLEhistorynullrangename_timestamp_idx,name_status_idxname_timestamp_idx767null402100.00Using index condition
0.00076794624328613 ms (with caching enabled)

idselect_typetablepartitionstypepossible_keyskeykey_lenrefrowsfilteredExtra
1SIMPLEhistorynullrangename_timestamp_idx,name_status_idxname_timestamp_idx767null603100.00Using index condition
0.00053095817565918 ms (with caching enabled)

idselect_typetablepartitionstypepossible_keyskeykey_lenrefrowsfilteredExtra
1SIMPLEhistorynullALLnullnullnullnull140711.11Using where
0.00064992904663086 ms (with caching enabled)

Used Versions
PHP 7.1, Zend 3.0, Symfony 3.2, Laravel 5.2, PHPUnit 5.6, Doctrine 2.6