Biggles2022,
Are you using the Calendar app on a Mac? If so, is it possible that you have both your iCloud and Gmail calendar setup and you're sending/receiving the invites from the Gmail account? You can learn how to check this here:
"Set a default calendar
You can set one of your calendars as the default calendar. When you add an event using Siri or other apps, it’s added to your default calendar.
- Go to Settings > Calendar > Default Calendar.
- Select the calendar you want to use as your default calendar."
You can take a look at the full resource here: Set up multiple calendars on iPhone
We hope this helps.
Take care.