In, say, /etc/profile
you can set the prompt system-wide (and remember that you have to log out and log back in again for any changes you make to take effect):
# Get the name (without the domain part) of the host (this is fancy-schmancy)
export HOST="`uname -n`"
# Set the prompt system-wide
Note the use of double quotes and "sideways pipe" in the assignment of HOST and the use of single quotes in the assignment of PS1.
Ought to work for you this way (or modify as you see fit).
A bare-bones default might look like this:
And don't forget to define PS2 while you're at it
And then be sure to export them