Streams are rooted at a 2-level depth in the depot hierarchy. A stream will have a root like "//depotname/streamname".
Once you create a stream root, you can't change it. The shallow root depth is meant to discourage you from using the stream's root path as any kind of intelligent label. (The problem being that if you could use depot paths for classifying streams, you would invariably end up having to branch files when a stream's classification changes, which leaves you with convoluted branching history.)
If you need to implement a stream naming scheme, you can use the stream Name field., e.g.:
Stream: //depot/ProductGizmo
Name: ClientAcme-ProductGizmo
Stream names can be changed. The name is displayed in P4V, and you can search by name. E.g.:
p4 streams -F "Name=*Acme-*"
However, you can't use the name in commands as a substitute for the depot path.
You could also overload the 2nd path in the stream root with your naming scheme. E.g.:
//depot/ClientAcme-ProductGizmo
That is pretty much like using a deeper depot path, because it can't be changed, and you can use it in commands, e.g.:
p4 changes -m1 //depot/ClientAcme-...