Be careful with this one.

we have tables with 6 million rows and doing

WHERE (CustomerName = @CustomerName OR @CustomerName IS NULL)

killed perfomance. The query took more than 2 minutes.

User dynamic SQL with EXEC or SP_EXECUTESQL.

watch out for single quotes with EXEC, to prevent SQL Injection and to deal with certain last names.

O'Malley in SQL is 'O''Malley'

IF @CustomerName IS NOT NULL

BEGIN

    SET @sql = @sql + N' AND CustomerName = ''' + REPLACE(@CustomerName,'''','''''') + ''''

END