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Well, it depends on WHICH database you are using.
With MySQL, you could use a regular expression to easily do this:
SELECT ... WHERE name REGEXP 'a.*?,' ...
SELECT .... WHERE name REGEXP 'a[^,]*,' ...
(says "find an 'a' followed by any number of characters followed by a comma" -- so 'a' has to be in the last name)
In SQL Server, it would be more complex. Something like
WHERE CHARINDEX( 'a', name ) > 0
AND CHARINDEX( 'a', name ) < CHARINDEX( ',', name )
WHERE INSTR(name,'a') > 0
AND INSTR(name,'a') < INSTR(name,',')
You could, of course, use the CHARINDEX technique with MySQL, too, but the REGEXP would be easier.