Yes, you will need to notify USCIS of any changes of address within 10 days from the date of the change by submitting a Form AR-11, Alien’s Change of Address Card. You should also notify in writing the asylum office with jurisdiction over your case of any change of address.
If you were conditionally granted by an immigration judge or the BIA, you will also need to notify EOIR (either the Immigration Court or the Board of Immigration Appeals, whichever last had jurisdiction over the matter) within 5 days from the date of the change of address. You will need to submit either Form EOIR-33/BIA or EOIR-33/IJ, Change of Address Form, which are available at the Immigration Courts or from the EOIR Internet website.
USCIS and EOIR will notify you of fingerprinting appointments and final approvals at the address you provide. Failure to properly notify USCIS, and where applicable, EOIR, of a change of address may result in a delay or termination of your eligibility for a final grant of asylum.