Counting unique text cells from muliple specific columns?

In all honesty for a single cell calc I think you would want/need a User Defined Function (VBA).
IMO native functions will struggle to handle the non-contiguous sets.

I've been looking at this for a while and though it's relatively straightforward to create a matrix in which names within even columns are discounted, ie:

INDEX(REPT(A1:D5,MOD(COLUMN(A1:D1)-COLUMN(A1),2)=0),0)

utilising that array of values within a unique count is proving beyond me I'm afraid... others may have other ideas.

A user defined function on the other hand would be pretty straightforward, ie:

Function UniqueNames(rngNames As Range, Optional boolCS As Boolean = False) As Long
    Dim vbComp As VbCompareMethod, rngCell As Range, strNames As String
    vbComp = IIf(boolCS, vbBinaryCompare, vbTextCompare)
    For Each rngCell In rngNames.Cells
        If rngCell.Value <> "" Then
            UniqueNames = UniqueNames - (InStr(1, strNames, "|" & rngCell.Value & "|", vbComp) = 0)
            strNames = strNames & "|" & rngCell.Value & "|"
        End If
    Next rngCell
End Function

the above, stored in a standard Module in a Macro Enabled file, can be called from a cell along the lines of:

=UNIQUENAMES((A1:A5,C1:C5))
note use of brackets encasing the non-contiguous ranges

you can pass an optional 2nd argument to stipulate case sensitivity - presumed insensitive (FALSE) unless otherwise specified

pb71, that is open to error I'm afraid should a name in either A or C be repeated in either B or D.

sailepaty's formula works but is as I am sure he/she would agree limited in scope - ie additional ranges would be cumbersome.

If flexibility is required then personally I think a UDF is only viable option - but that's my opinion of course

ha - serves me right for not testing either

adapting the earlier approach

=SUMPRODUCT(((A1:A5<>"")/(COUNTIF(A1:A5,A1:A5&"")+COUNTIF(C1:C5,A1:A5&"")))+((C1:C5<>"")/(COUNTIF(A1:A5,C1:C5&"")+COUNTIF(C1:C5,C1:C5&""))))

but again of very limited scope... and not particularly efficient

Differentiating by format is generally ill advised, however, I'm still not entirely sure I follow all the requirements.

Are you saying that you wish to have the option within the UDF call to include cells based on a pre-requisite font format and/or character ?

how about using more func addin http://download.cnet.com/Morefunc/30...-10423159.html
=SUMPRODUCT(--(UNIQUEVALUES(ARRAY.JOIN($A$1:$A$5,$C$1:$C$5))<>""))
Or to ignore case
array entered
=SUMPRODUCT(--(UNIQUEVALUES(ARRAY.JOIN(LOWER($A$1:$A$5),LOWER($C$1:$C$5)))<>""))