How to pass objects from cells? OR how to make the sub interpret what I pass from cell as object?
Cells don't contain Objects, they contain text or numbers. Your code must be able to use Strings.

Cell.Value = "Macro1, Sheet1, Tbox1"
Sub MacroName(wsName as String, TBoxName as String)
With Worksheets(wsName). Controls(TBoxName)...
Then 

Application.Run Arr(0), Arr(1), Arr(2)
In your example Arr(0) = "DisplayNameofTextBox", Arr(1) = "ws", and Arr(2) = "activeTbx". Neither "ws" nor "activeTbx" are Objects

Reread the opening line of Paul's signature. "Tell us WHAT you want to do, not HOW you think you want to do it"