How to get the number of rows or columns in a merged cell?

I don't think the range is named before you merge it that or either only the top left most cell of the range is named before merge - in either case you would get 1 as you outline.

Merged cells do not work quite as people think - in reality the content of the merged area generally resides only in the top left most cell of the merged area.

=A1

will return value of zaza

=A2

will return nothing (blank/0) assuming it (A2) was empty prior to being merged.. although part of the merged area it is itself devoid of content - the content exists only in A1

So ... my point was basically... if you had A1:D5 highlighted, then named, then merged - ROWS and COLUMNS would return the expected values.

I'm not sure, off hand, is there is a native function you can use to determine the address of a merged area if the area is named after the merge or only the top left cell is named before merge ... I think you would be looking at VBA
(things are also complicated of course by the fact that any given name can cover multiple non-contiguous areas - merged or not)

Function RCX(rngX As Range, bType As Byte) As Long
    Dim rngArea As Range, rngUnion As Range, rngRC As Range
    On Error Resume Next
    For Each rngArea In rngX.Areas
        Set rngRC = rngArea.MergeArea
        Set rngRC = IIf(rngRC Is Nothing, rngArea, rngRC)
        If bType Then
            Set rngRC = rngRC.EntireColumn
        Else
            Set rngRC = rngRC.EntireRow
        End If
        If rngUnion Is Nothing Then
            Set rngUnion = rngRC
        Else
            Set rngUnion = Union(rngUnion, ComplementLoop(rngRC, rngUnion))
        End If
        Set rngRC = Nothing
    Next rngArea
    If bType Then
        For Each rngRC In rngUnion.Columns: RCX = RCX + 1: Next rngRC
    Else
        For Each rngRC In rngUnion.Rows: RCX = RCX + 1: Next rngRC
    End If
End Function

'below Function c/o Andy Pope
Function ComplementLoop(rngA As Range, rngB As Range) As Range
    Dim rngX As Range
    Dim rngC As Range
    For Each rngX In rngA
        If Intersect(rngX, rngB) Is Nothing Then
            If rngC Is Nothing Then
                Set rngC = rngX
            Else
                Set rngC = Union(rngC, rngX)
            End If
        End If
    Next
    Set ComplementLoop = rngC
End Function

stored in a Module in VBE, called from a cell along the lines of:

=RCX(zaza,0)

where the first parameter is the range of interest and the second (0,1) stipulates whether you're returning Rows (0) or Columns (1) ... for a non-contiguous range like A6:C7, B12:C13 the above would return 4 for rows and 3 for columns.

I'm sure there are far more elegant and robust methods out there to do this kind of analysis though.

EDIT: code corrected - missing a release of rngRC in the Loop