You can set the Magento search in admin>system>configuration>catalog>search to min of 3 characters. However you’ll probably find that after changing this setting you still get NO results for a 3 letter word.

You’ll probably also need to change the mySQL full text word length variable ft_min_word_len. By default this value is 4, resulting in 3 character words not being indexed.

To change the full text word length variable to 3 add this to your my.cnf:

ft_min_word_len=3
Restart mysql

# service mysqld restart
Finally reindex the magento catalog, you can do this via GUI or command line.

$ php magento/shell/indexer.php reindexall
After the reindex completes you should be able to search your magento store succesfully with 3 character search terms.

Source: https://www.linuxconsultantsireland.com/content/magento-product-search-using-search-term-less-4-characters-returns-no-results