I am constantly scanning the Power Automate community site and I see certain question repeatedly pop-up. One of those questions is how to send an email from Power Automate that doesn't come from the Flow author. There are a number of options as I will explain below.
By default, when sending an email using the Office 365 Outlook Send an email (V2) action that the connection determines who the email will be from. When adding an action the connection for the Flow author is automatically used. So, if I author the Flow, the email will be from me.
To change who the email is from, you have two options.
Add a connection
The first option is to create a connection for the additional account. You'll need the users email address as well as password to add the connection. To add the connection, click on "Add a new connection" under "My connections.
You will be prompted for the the email address and password associated with the account. Once that information is provided, a new connection is created and automatically selected for this action.
Once the connection has been created, it can be selected at any time in this or other Flows for any action that requires a connection. With the new connection selected, emails sent from this action will be from the account associated with the new connection.
Use the "Send as" feature
Another option is for you to use the "Send as" option. You'll need to click on "Show advanced options" to configure "Send as".
To use this option, you are required to have "Send as" permissions granted to you in order to send an email which shows as being from that account.
Shared Mailbox
Rather than using the "Send an email" action, you might also consider using the "Send an email from a shared mailbox (V2)" action. Obviously, you need to have a shared mailbox and have permissions to send an email from that shared mailbox. The email will show as being sent from the shared mailbox and not the Flow author. An advantage of using this that no additional Microsoft 365 licenses are being used - there is no cost for a shared mailbox.
The final option available to you without purchasing third party connectors or services is to use the "Send an email notification" action. Emails sent using this action show as from "Microsoft Power Apps and Power Automate".
None of the options that I have presented are better than any other option. The choice is totally dependent on you specific requirements.