... why the domain name is not encrypted when a request do a DNS Server is made.
DNS is an old protocol which predates the massive use of encryption on the internet. It was designed at a time when the peers in the network were usually considered trusted or at least not malicious. There are actually alternatives which encrypt the names, like DNS over HTTPS, DNS over TLS or DNSCurve.
And could we solve the USA net neutrality problem with just encrypting the domain name?
Net neutrality is more about preferring one kind of traffic against other kinds and less about blocking illegal content (which is usually explicitly allowed even with net neutrality). Even if you encrypt the domain name the source and target IP of the connection, the used ports and the traffic pattern are still visible to the ISP and can be used for categorization of traffic. Also, the ISP might let preferred customers mark their traffic in a specific way so that it gets priority. Thus, hiding DNS from the ISP will not help much with net neutrality. It might help with privacy though, i.e. making it harder for the ISP to use or sell behavior information about your internet usage.