A summary report based on that table is the simplest to set up. You sort your records by the name field and use a summary "count" field placed inside a sub summary layout part "when sorted by" the name field. As long as your records are sorted by the name field, the sub summary layout part is visible and appears once for each unique value in Name with the count of records for that name. The individual records can be listed with the sub total or hidden.
And there are other ways to get such subtotals: Sum_Calculation based on condition
And now that we have FileMaker 12, ExecuteSQL() can be used: Creating Filemaker Pro summary reports--Tutorial
I have to admit that I never really bothered to get familiar with the term "parts" of a layout. Actually the first thing I've done so far is to delete always the header and bottom from the default new FM-File. As you hinted the summary parts in the layout are indeed what I need and it's simple once you've spend some time to learn that set-up.
I have also added some scripts for sorting the field I need information of an run the scripts via Buttons.
What confused me at the beginning of my search was an example on Filemaker's own website
Here they suggest to use a reciprocal value to get the TOTAL (???) count
Next, create a calculation field called "Counter" with the following expression:
1 / Count (SelfJoin::LocationField)
I just does not make any sense to me to get the result from 5 records in form of the value 0.2
It's an older method of counting unique values.
If your table had these records:
This method computes a value of 3 (apple, orange, strawberry)
But in FileMaker 12, you can get the same count much more simply using EsecuteSQL with the DISTINCT keyword: A new way to count unique values in FileMaker 12