Yesterday I changed my domain's name server from cloudflare to dnspod. And I used dig to test it. But the ANSWER SECTION is always the old name servers.
;; AUTHORITY SECTION:
amazingjxq.com. 21336 IN NS kim.ns.cloudflare.com.
amazingjxq.com. 21336 IN NS brad.ns.cloudflare.com.
Is the ANSWER SECTION stand for name servers? If so why is it not changed?
The Authority section indicates the server(s) that are the ultimate authority for answering DNS queries about that domain.
The reason for this section is that you can query any* DNS server(s) to answer a query for you. That server may choose though to answer the query from a cache. However, if you want to ensure you get an authoritative response ("from the horses mouth" so to speak) - you should ask the server(s) in the authority section.
(* = Any server which will accept your query, that is.)