How to send documents internally for signature, and once signed send to individual recipients, so that the recipients cannot see other recipients documents?

Hello ​@SarahMason 
Thank you for reaching out, and welcome to the Docusign Community!
Yes, there is a tidy way. You can send all documents in a single envelope and enable Document Visibility so each recipient only sees the document assigned to them. This allows you to manage everything in one envelope while keeping each recipient’s document private.

Note: Some advanced features and options are supported only in certain Docusign plans. Your account plan might not support some options discussed in this help topic. For more information about which options are available for your account, contact your account administrator or Docusign Customer Support. Visit our Contact Support web page for contact options to reach Customer Support.

Here are related articles for your reference.
Set Document Visibility
 Use Document Visibility to Control Recipient Access
Account Settings for Document Visibility
Some Things To Know About Document Visibility

Sincerely,

Ma. Cassandra | Docusign Community Moderator
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Hello ​@SarahMason 

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Sincerely,

 Ma. Cassandra | Docusign Community Moderator
If this helped. Feel free to Like👍and click "Best Answer."