Although a Sub name same as built in ones are not recommended, you can do what you are after like below.
First you need to change the InputBox Type to 2 (String), since you are comparing with String. Then you should make a function to check if the input is part of a Manager List.
Sub inputbox()
On Error Resume Next
Dim Manager As String
Manager = Application.inputbox(Prompt:="Please enter a manager name:", Title:="Pick A Manager Name", Type:=2)
If Manager <> "" Then
If IsManager(Manager) Then
MsgBox "Your input was " & Manager
Else
MsgBox "Incorrect Name, pick a new one!"
End If
End If
End Sub
Private Function IsManager(sTxt As String) As Boolean
Dim aManagers As Variant, oItem As Variant, bAns As Boolean
aManagers = Array("Ben", "Cameron", "Chris", "Martin", "Peter")
bAns = False
For Each oItem In aManagers
If LCase(oItem) = LCase(Trim(sTxt)) Then
bAns = True
Exit For
End If
Next
IsManager = bAns
End Function
UPDATE (Improved version suggested by Simon1979):
Private Function IsManager(sTxt As String) As Boolean
On Error Resume Next
Dim aManagers As Variant
aManagers = Array("Ben", "Cameron", "Chris", "Martin", "Peter")
IsManager = Not IsError(Application.WorksheetFunction.Match(Trim(sTxt), aManagers, 0))
End Function