Multisite Navigation Menu (site selector UI)

I have a connected multisite that has a main site and 2 sub-sites that all make up sections of one larger site. As such, the "site names" all begin the same. 

There is only so much horizontal room next to the tiny thumbnail representing each sub-site for the site's name in order to differentiate them from each other as, in my case, they are truncated and look identical. Unless I squint at the thumbnail (which has the same colour scheme) it's not easy to tell them apart. 

One suggestion would simply be to show the full name of the site/sub-site on hover much like what you do for the the longer plugin names.