If I login over the network, my terminal type is set to "sun"/"AT386"

How can I change that? In SunOS 4.x the type would have been "network"

If no terminal type is specified in the network (telnet/rlogin)
protocol, the standard startup scripts (/etc/profile, /etc/.login)
will set the terminal type to the default console type (sun for
SPARCs, AT386 for x86).

To get the SunOS 4.x. behaviour back, all you need to do is set the
type to "network", if not previously set.