Debbie wrote...
Flint Dianne
Jones Amber
Jackson Dorraine
Smith Laurel
Smith Lesley
Smith Lesley
Smith Lesley
Jones Amber
Jones Amber

If these are my names and I use any of the formulas suggested the
result
returned is 5 and it should be 6??
....

There are only 5 distinct names.

Flint Dianne
Jones Amber
Jackson Dorraine
Smith Laurel
Smith Lesley

If you mean the 2nd name, the 1st instance of Jones Amber, should be
considered distinct from the 8th and 9th names, the 2nd and 3rd
instances of Jones Amber, then it actually gets easier. If these names
were in A1:B9, use the formula
=1+SUMPRODUCT(--(A2:A9&B2:B9<A1:A8&B1:B8))