My name is Rae and I work for Shopify. Thanks for reaching out about this, and welcome to the Community!
There are a couple of different reasons why your name might be showing up on draft order invoices that are emailed to your customers. However, so that I can get a better idea of where your name is visible, can you please send me a screenshot that shows the notification and where your name is included? Feel free to blur out any sensitive details on the notification before sharing it here.
In the meantime, one setting that may be adding your name to this template is tied to the details that are listed as your store name in the 'Settings > General' section of your Shopify admin. In this section, under 'Store name' or 'Legal name of business' is your name listed anywhere? If so, please remove it and replace it with your store name instead.
Another thing that might have caused this to happen is if there have been coding changes made to the draft order notification template and an extra variable was added that is pulling your name into the notification. Some of the variables that would pull these details are the 'user' and 'user.name' variables. Please check this template to see if any of these variables have been added to it.
If you haven't edited the coding and you're using Shopify's default draft order notification template, then you may want to revert the template back to its default settings. However, please keep in mind that if you have custom coding here, or if you've made any changes to this template at all, reverting the template will wipe those changes. If you're unsure if this template has been edited, then I recommend not reverting the template to avoid any potential risk of losing customizations. If you would like to revert the template, please do this by heading into your admin and clicking on 'Settings > Notifications > Draft order invoice'. Then, scroll to the bottom of the page and click 'Revert to default'.
Looking forward to hearing from you with a screenshot so that I can look into this further!