Hi there, jdelvie.
For now, you can only search by customer's name when creating an invoice through the Plus (+) icon. Though, you can go to the Customer Center and search for the name of the company. Then, create the invoice from there. Here's how:
Let's also send your feedback about adding more search options when creating invoices. Just click the Gear icon and select Feedback. All product feedback will be collated and will be sent to our engineers.
We're always here if you need more help with QuickBooks Online.