To distinguish two Firefox profiles that I run simultaneously, I use different themes on each. For Firefox this might actually be the best way.

For a file manager (I assume the Dolphin you’re talking about is the file manager), the closest I remember seeing is a red toolbar on the unrelated Nemo file manager when it’s run as root.

If Dolphin is per-user theme-able, then you could do what I do with Firefox. If it supports other kinds of plug-in, then maybe there’s one that does what you want already.

To my knowledge, windowing systems can’t override the title of an application’s window, and even if they could, the application could change it back again at any time, creating a race condition, or a very ugly situation where the system picks and chooses which windows are allowed to modify their titles and which ones aren’t.

Therefore, I think you’d have to write your own plug-in (if they’re a thing and the API permits title modifications), modify Dolphin’s source code yourself or submit a feature request to Dolphin’s developers, cross your fingers and wait.