Hi daleldalel,
Since you're having an issue with the invitations being sent from your iCloud alias instead of your main email address, we recommend that you try the steps here: Add and manage email aliases for iCloud Mail on iCloud.com
To perform the recommended troubleshooting steps via the link above, complete the steps in the section titled "Turn off, turn on, or delete an alias."
You can turn an email alias on or off at any time. You can also delete email aliases that you no longer want to use. While turning off an email alias is temporary, deleting it is permanent. When an alias is turned off or deleted, email sent to that alias is returned to the sender.
1) In Mail on iCloud.com, click 
at the top of the Mailboxes list, then choose Preferences.
2) Click Accounts, select an iCloud Mail alias in the list, then do any of the following:
*Turn off an alias: Select “Disable alias.”
*Turn on an alias: Deselect “Disable alias.”
*Delete an alias: Click “Delete alias,” then click Delete.
3) Click Done.
We recommend the steps above because deleting your iCloud alias could help to resolve your issue.
Once you delete the iCloud alias, test to see if you can send the HomeKit invitation from your main email address.
Share control of your home
To invite someone to control your home, follow these steps:
1) Open the Home app on your iPhone, iPad, or Mac.
2) Tap or click the More button 
, then select Home Settings. If you have multiple homes set up, choose the Home that you want to invite someone to, then select Home Settings.
3) Tap or click Invite People.
4) Enter the person's Apple ID that they use with iCloud.
5) Tap or click Send Invite.
Find out what to do if you can't invite someone to control your home.
If the original problem persists after trying the previous steps, please provide us with specifics on what you see for more help, and we will continue from there.
Thanks for using the Apple Support Communities.
Cheers!
