Hi Byron,
               You can do it by using For each loop container.Basically divide the whole work into two parts.First Generate the excelsheet and create sheet names using Execute SQL Task and insert the data into excel sheet using DataFlowTask.

1.First list out all customer names and save it to Object variable using ExcuteSQL Task.
2.Next step,add forreach loop container and select ForEachAdo Enumarator.
3.Go to -->Variable Mapping --> Map Customer name to one variable.
4.Take execute SQl task inside Foreach loop container. -
         -> Choose connectionType --Excel 
        --> Connection -- create excelconnection manager and select that connection.
        --> SQLSourceType -- Variable
        -- > Create a variable and build expression like below
"CREATE TABLE `"+(DT_STR,20,1252) @[User::VariableName] +"` (
  `Column1` NVARCHAR(255),
  `Column2` NVARCHAR(255),
  `Column3` NVARCHAR(255),
  `Column4` NVARCHAR(255),
  `Column5` NVARCHAR(255)
)"
  This will create a excelsheet with customername as sheetname.

5.Create DataFlowTask and
      --> Source query pass customer name in where clause
      -- Target as excelsheet and sheet name UserName.

You can create excelsheet dynamically by building expression and passing that expression value to excelconnection manager.