There is a ticket to allow multiple renaming scripts for manual selection (PICARD-524) and also a more generic ticket for allowing multiple settings presets (PICARD-9).
The way this is usually done by now is to make it automatic using the scripting. You can have your script name things differently based on any criteria, e.g. you can choose to have different naming rules for various artist releases, for singles, for videos, for standalone recordings etc.
E.g. the default naming script already makes a slight change by including the artist name in file names if the release has more then one title by using
$if(%_multiartist%,%artist% - ,).
A typical use case if having compilations named differently, use something like this:
$noop(Various Artist albums)
$noop(Single Artist Albums)
Instead of checking for compilations with
$eq(%compilation%,1) you can also e.g. check for a specific type, e.g. single with
$inmulti(%releasetype%,single) or check for video files with
$is_video() and many more.