It is not easy in some user installs to identify the right site for each language. It would be helpful, it is possible the Alternative Title would be use in the Site Name of the Admin Bar.

Currently helps this plugin.
https://gist.github.com/bueltge/7abfbfc65f1f19a782cc

But, will we add this to the core. The result is a optional settings or not? Or we use it always, if is set in the settings to each site?