Splitter refers to signal duplication ability, you don't need that functionality.
A Matrix Switch will allow you to direct each input to a different screen but it won't intrinsically allow you to drive multiple screens from one input so you'd four outputs from each laptop going into the switch - if you're wiring it up to four different locations you're potentially dealing with 16 inputs to switch between.
You could also make sure of the screen's build in switches, if it's controls are accessible. For example if each screen has four inputs then you could route one to each potential laptop position .
The feature behind both daisy chaining and (some) hubs and docks is called MST, which is a feature in the Displayport standard that allows one port to have multiple independent screens connected, up to the maximum bandwidth of that port.
I believe it's also limited to the total number of displays supported by the computer's graphics chip - Three for the most common Intel graphics.
Provides information about Multi-Stream Transport (MST) support for Intel Graphics.
www.intel.com
Will you be speccing the laptops too, or do you know which models will be used? DisplayPort support is common but far from ubiquitous while alternative manufacturers of graphics chips aren't as common.
If you need something that works with every laptop then external USB graphics chips are probably the way to go, technologies such as Display
Link (not to be confused with Display
Port). They're not quite as smooth as a normal video output but unless you need low latency they're often good enough.
4-way ones aren't all that common but you can use multiple ones, the DisplayLink software supports 6 screens on Windows and 4 on Mac OS:
DisplayLink Graphics Our DisplayLink technology makes it simple to connect any display to any computer that supports USB or Wi-Fi and provides universal solutions for a range of corporate, home and embedded applications where easy connectivity of displays enhances productivity. With DisplayLink...
www.displaylink.com
(I don't think it supports ChromeOS, as found on Chromebooks, but I'm not sure if anything does).
These are often called docks as well, and confusingly those docks with the new USB Type C connector can operate their video outputs over either MST or USB as USB-C has an alternate mode which allows it to output a DisplayPort signal (which is optional, but common enough plenty of things use it).