Is there a way to assign transactions in a trust account to specific customers/accounts numbers?

Hi there, aidin1.

Both journal entries and bank deposit will let you associate a customer transaction to a trust account. Use these articles as a guide on how you can record it: 

• Create a journal entry in QuickBooks Online
• Record and make Bank Deposits in QuickBooks Online

However, if the trust account is a form of an advanced deposit, follow the steps in this article on how you can properly track this type of transaction: Record a retainer or deposit. 

Let me know if you need anything else.