Can you filter a GET search field based on a String value?

Looking to search a field's result for specific results.
So if I have a name field and want to find names beginning with A, I should be able to input 'A*' and it'll bring back all names beginning with A. So far I've only been able to pull back all names inside of the name field itself, so it doesn't matter what the input string is.

Can anyone point me in the right direction of how to set this up?

Thanks