Yes.
However, when you say "it should be able to associate the correct / original software in the database for each client," this depends on what feature you're talking about. For example, if you defined your Detection Rule for a software package by the .exe name, someone renaming it will obviously stump you. Instead, look for registry keys that show it's installed (such as HKLM\SOFTWARE\Microsoft\Windows\CurrentVersion\Uninstall) or something more involved (like .exe AND .dll versions at a particular path).
On the other hand, if you create an Application Metering policy, you can look for Internal Name. This is something that users cannot change, even if they rename videogame.exe to excel.exe. The internal name hasn't changed, so Altiris still knows and will meter the application based on that.
So it all depends on what kind of data you're talking about. If you build things properly, I can't imagine this would be an issue. Did something particular come up in your environment that you're wondering about?