Hide all output from a background process
You can use a subshell to get rid of the job control messages:
$ alias alertme="xmessage Alert!"
$ ( alertme & )
$
If your commad also produces some output to STDOUT and/or STDERR, pipe those to /dev/null:
$ ( alertme > /dev/null 2>&1 & )
A slightly neater version of another answer here:
(&>/dev/null alertme &)