You can certainly customize the prompt.
From the documentation:
The prompts psql issues can be
customized to your preference. The
three variables PROMPT1, PROMPT2, and
PROMPT3 contain strings and special
escape sequences that describe the
appearance of the prompt. Prompt 1 is
the normal prompt that is issued when
psql requests a new command. Prompt 2
is issued when more input is expected
during command input because the
command was not terminated with a
semicolon or a quote was not closed.
Prompt 3 is issued when you run an SQL
COPY command and you are expected to
type in the row values on the
terminal.
If you want to set the prompt on a per user basis, you can add the \set commands to the user's .psqlrc file.
So, your $HOME/.psqlrc would be something like this:
\set PROMPT1 '(%n@%M:%>) %`date +%H:%M:%S` [%/] \n%x%# '