Actually the date, which is present, is global information too. 
Nevertheless I've found in your Wiki the solution:

http://wiki.horde.org/DisplayUserName?referrer=HowTo

and this is what I'd like to have in Horde distribution. Looks like 
somebody (i.e. this Wiki page author) had the same need as me.

Of course removal of username from the right side of topbar at portal 
page would be needed too, for simplicity.

Which is why we display it on the portal. Since we use this space 
already for application-specific information - as you noticed - it's 
bad UI to put global information there, but not always.

There is black bar almost on top of Horde screen. There is date at the 
bar's left side. There is username at the right side on the portal 
screen. However, on the application screens username is not displayed 
on the bar. Sometimes there is other information displayed, such as 
quota and folder name in IMP. However in other applications the bar is 
almost empty.

I'd suggest to make username (current identity)  visible _always_ on 
the bar. Using more than username, knowledge who is really logged in 
is clearly needed.