The recommended Microsoft solution is to create a separate account. However, if your solution is small, you can instead add the 'IIS APPPOOL\DefaultAppPool' user as a database user in your SQL instance, then providing the proper 'User Mappings' to the databases you need the DefaultAppPool user to access.
You may not necessarily be able to search for this user, but you can still enter it in the 'Login name' field in the "Login - New" window as "IIS APPPOOL\DefaultAppPool" (without the quotes).
MSDN Reference at:
http://social.msdn.microsoft.com/Forums/en-US/sqlsetupandupgrade/thread/73eee0b4-9eee-4a71-a448-3e3eef9ee404/[
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