This thread has been very helpful to me lately. Just to extend on the answer by @RubberDuck, the File System Object in the Microsoft Scripting Runtime library is already there to achieve this. Also if you define it as an Object as below, it will save you the hassle of having to enable 'Microsoft Scripting Runtime' in VBA Tools > References:
Dim fso As Object
Set fso = CreateObject("Scripting.FileSystemObject")
Debug.Print fso.GetBaseName(ActiveWorkbook.Name)
In this way it will return name of the ActiveWorkbook without extension.
There is another way by using INSTRREV function as below:
Dim fname As String
fname = Left(ActiveWorkbook.Name, InStrRev(ActiveWorkbook.Name, ".") - 1)
MsgBox fname
Both will return the same result. Also in both of the methods above, they will retain any full-stops in the file name and only get rid of the last full-stop and the file extension.