Is it possible to control which monitor is considered the primary monitor?

Often your monitor setup can be found in the Xorg configuration file /etc/X11/xorg.conf.

However, many modern distributions (such as recent Ubuntu releases) try to avoid using a configuration file, since maintaining it can be a pain. You can create this file initially by running:

# Xorg --configure

From there you can make further customizations. The Arch wiki has an article that should help with making customizations.

If you want to change your primary monitor without editing xorg.conf you can try the following:

 $ xrandr --output XXXX --primary

Here XXXX should be replaced by the output you want to be primary. You can run

$ xrandr --current

To see the current configuration and see what output devices are available. Typically these will have names like "VGA1", "LVDS1", or other names that refer to the connection that is used.

Setting the monitor as primary will typically move your panels over as well, which is nice if you are using a laptop and want to change which monitor is the primary monitor multiple times a day. I find this a lot nicer than creating an xorg.conf file, but my monitor configuration changes multiple times a day.