How do I get it to take a concatenated string?
You don't, and you can't. PumpSP is an Object, not a String. The only thing you can ever Set it to, is an object reference.
This is very similar to, say, how you would access the controls on a UserForm:
Set box = Me.TextBox1
The reason you can get that object with a string, is because a form has a Controls collection that lets you provide a string, works out which control has that name, and returns the Control object for it:
Set box = Me.Controls("TextBox" & i)
So in your case to go from this:
Set PumpSP = ThisDisplay.PumpSetpoint1
I don't know what ThisDisplay is, but maybe it has a similar collection:
Set PumpSP = ThisDisplay.Controls("PimpSetpoint" & i)
If there's no collection that lets you retrieve items by name with a string literal, you're out of luck.
Set PumpSP.name = "ThisDisplay.PumpSetpoint" & "1"PumpSetpoint1in to find it.