This is Finley from the Shopify support team, thanks for reaching out about this!
Change the logo on your email templates
From what you shared, I understand that you've updated your logo in the theme editor, so it is showing correctly on your website. However, your old logo is still appearing when sending out any email notifications, is that right?
If so, the logo you see on your email templates needs to be updated from your Shopify Admin > Settings > Notifications > Customize like so:
For reference, we also have this guide.
Add a logo to your packing slip
Your packing slip template is set up to have your store name in text only, so if you'd like, you can choose to:
1) Add your logo and remove your store name
2) Add your logo above your store name
3) Add your logo next to your store name
The Order Printer App
If you'd like to print invoices and packing slips from an order page in your Shopify admin, as well as print these in bulk (up to 50 orders at a time), you may be interested in adding our free order printer app. You can customize these order templates to add your logo as well.
I hope you found this helpful! Just let me know if you have any further questions. If you're unable to update the logo as expected, please let me know where you're seeing the old logo and I can take a closer look.