Sometimes people do not like the appearance of a Class A chimney on the outside of their home. What is very common is to build a wooden chase around the factory built chimney. This way you can use whatever material you would like to finish off the chase. You can use cultured stone, stucco, siding or another suitable material that matches your home. Whatever building materials you use, make sure you maintain your clearances to combustibles.
Wooden chase with cultured stone installed only from the roof up. This still needs a chase cover.
To finish off the top, cover using a stainless steel chase cover. A storm collar will also be needed to keep water from entering around the chimney pipe.. Every stainless steel chase cover is custom made. Call and order one from a reliable chimney supply company.
It is always a good idea to insulate the chase. Also as always make sure you maintain your clearances to combustibles using wall straps.