Assuming that you have allowed the operating system to configure the primary interface for you, there are three (3) files you must change:

/etc/hosts
/etc/nodename 
/etc/hostname.

will be the primary ethernet interface for the system. Some examples (depending on your architecture) will be bge0, hme0, e1000g0, eri0, qfe0. Here’s an ad-free answer for future reference. Also change the savecore directory to reflect the new hostname in /etc/dumpadm.conf, and you may also need to edit /etc/inet/ipnodes, depending on the exact version of Solaris.

You can then do a

#svcadm restart network

to apply changes without the need to restart your system.