I want to use Xfire (www.xfire.com) to log how many hours I spend on playing each game:

Xfire->Options->Game Library shows these three games correclty with correct icons:

Ultima I: The First Age of Darkness
Ultima II: The Revenge of the Enchantress
Ultima III: Exodus

When I play Ultima I: The First Age of Darkness, Xfire shows my status playing Ultima I: The First Age of Darkness
When I play Ultima II: The Revenge of the Enchantress, Xfire shows my status playing Ultima I: The First Age of Darkness
When I play Ultima III: Exodus, Xfire shows my status playing Ultima I: The First Age of Darkness

I would like to have different hour logging for each game, because I complete them all, so what can I do?

I think problem might be related to the fact that all those games share the same file at:
C:\GOG Games\Ultima Trilogy\DOSBOX\DOSBox.exe

Ultima IV: Quest For Avatar shows its status correctly but it is autodetected in a different folder for DOSBox
c:\program files (x86)\GOG.com\Ultima 4\DOSBOX\dosbox.exe

Worst case you should be able to make three copies of it named: DOSBoxI.exe, DOSBoxII.exe, DOSBoxIII.exe and update your shortcuts accordingly.

Uninstalled the whole thing
Clicked setup_ultima_trilogy_2.0.0.7.exe
Clicked Options from the bottom left corner
Unticked Ultima 1 and Ultima 3
Clicked Install
Clicked Xfire Options->Game Library->Detect Games
Launched Ultima 2
Now Xfire detects Ultima 2 and shows correctly showing Ultima II: The Revenge of the Enchantress

This is a nice workaround, since there is no real reason to have all 3 of them installed simultaneously.