One thing I spotted off the bat:

If Cells(row, index).Value = name Then

The variable passed to the function is named rowNumber, not row. Change that line to:

If Cells(rowNumber, index).Value = name Then

edit:

One other thing to note is that your function never actually stops on its own. The only reason it ever ends is because it runs into an application defined error when trying to read column 16385 (because Excel is limited to 16384 columns*), which immediately kills the function, returning a #VALUE error.

The following revision prevents that and returns a -1 if the requested column name is not found:

Option Explicit

Function FindColumnIndex(name As String, rowNumber As Integer) As Integer
    Dim index As Integer
    index = 1
    Dim found As Boolean
    found = False

    FindColumnIndex = -1

    Do While found = False
        If Cells(rowNumber, index).Value = name Then
            FindColumnIndex = index
            found = True
        End If

        index = index + 1
        If index > 16384 Then Exit Do
    Loop

End Function

[ * Excel 2007 is thus limited, anyway. I have no idea if newer versions have larger limits or not.]

If you run the following test:

Sub Test()
    Dim d As Double: d = 0.5 + 0.00024575 * 10000000
    
    Debug.Assert d = Int(d)
    Debug.Assert 0.5 + 2457.5 = Int(0.5 + 2457.5)
    Debug.Assert 0.5 + 0.00024575 * 10000000 = Int(CDbl(0.5 + 0.00024575 * 10000000))
    Debug.Assert 0.5 + 0.00024575 * 10000000 = CDbl(0.5 + 0.00024575 * 10000000)
    Debug.Assert 0.5 + 0.00024575 * 10000000 = VBA.Int(0.5 + 0.00024575 * 10000000)
    Debug.Assert 0.5 + 0.00024575 * 10000000 = Int(0.5 + 0.00024575 * 10000000)
End Sub

You will see that only the last Assert fails. This is probably a compiler bug.

Note that Int is not the same as VBA.Int.

Edit #1

As suggested in the comments by @GSerg, it appears that the Int method (not VBA.Int) does indeed calculate at compile time and it probably uses a different floating point precision. For example:

Option Explicit

#Const Test = Int(12.5)

Sub TestPrecompiler()
    #If Test = 12 Then
        Debug.Print "Int method calculates at compile time"
    #End If
End Sub