The DNS uses protocol UDP.
The packets of UDP have biggest size (many times) until 576 bytes.
What's going on if a DNS name that it is sought does exceed this size?
It can be sent in two packets?

I'm unsure exactly what your issue is. The maximum length of a fully qualified domain name is 255 characters (octets) by RFC 1035 (http://www.faqs.org/rfcs/rfc1035.html).

The DNS uses protocol UDP.
The packets of UDP have biggest size (many times) until 576 bytes.
What's going on if a DNS name that it is sought does exceed this size?
It can be sent in two packets?

Huh?