index mysql concatenated columns
Two options I can think of. First, if you are on MyISAM or InnoDB 5.6+, you could store the concatenation in a separate field and use a FULLTEXT index on that field.

The other option is to index the first_name and last_name fields separately. Then change your query to:

WHERE a.first_name LIKE "twain%" OR a.last_name LIKE "twain%"


Removing the wildcard from the beginning will allow the indexes to be used.