How To Get Unique Records When There Are More Groups

Steve writes "I need a query to show all the medicare patients only. I want only one kind of insurance for each patient. I am getting records where each patient has more than one insurance like medicare and something else.
Each patient has one,two, three or more insurances like
medicare,medical,blue cross,tricare etc.

The result should look like this:
Sam pick Medicare
John white Medicare
Ann Richmond Medicare

My query retrieves patients with more than one insurance.

select patient_first_name f_name,patient_last_name l_name,patient_zip zip,
count(distinct payer_id) payer_id
from claims
where payer_id ='abcdefhj'
group by patient_first_name, patient_last_name,patient_zip
having count(distinct payer_id)= 1
order by patient_zip asc;

please help me. Greatly appreciate your response."