SUM of grouped COUNT in SQL Query

Try this:

SELECT  ISNULL(Name,'SUM'), count(*) as Count
FROM table_name
Group By Name
WITH ROLLUP

SELECT name, COUNT(name) AS count
FROM table
GROUP BY name

UNION ALL

SELECT 'SUM' name, COUNT(name)
FROM table

OUTPUT:

name                                               count
-------------------------------------------------- -----------
alpha                                              1
beta                                               3
Charlie                                            2
SUM                                                6

Without specifying which rdbms you are using

Have a look at this demo

SQL Fiddle DEMO

SELECT Name, COUNT(1) as Cnt
FROM Table1
GROUP BY Name
UNION ALL
SELECT 'SUM' Name, COUNT(1)
FROM Table1

That said, I would recomend that the total be added by your presentation layer, and not by the database.

This is a bit more of a SQL SERVER Version using Summarizing Data Using ROLLUP

SQL Fiddle DEMO

SELECT CASE WHEN (GROUPING(NAME) = 1) THEN 'SUM'
            ELSE ISNULL(NAME, 'UNKNOWN')
       END Name, 
      COUNT(1) as Cnt
FROM Table1
GROUP BY NAME
WITH ROLLUP

SELECT name, COUNT(name) AS count, SUM(COUNT(name)) OVER() AS total_count
FROM Table GROUP BY name