Dear Richard _
Welcome to Microsoft Community.
Based on your description, I understand that your account has been receiving unusual login messages. I understand your feel.
If you aren't sure about the source of an email, check the sender. You'll know it's legitimate if it's from the Microsoft account team at account-security-noreply@accountprotection.microsoft.com.
You can also check if there are indeed any unusual activity messages by logging into your account and going to the activity page. https://account.microsoft.com/privacy/activity-history
You can find out if the person has successfully logged into your account and if they have performed certain activities based on the type of activity.

You can refer to What is the Recent activity page? - Microsoft Support to get more details.
You can take the following steps to protect your account:
Change your account password.
You can go to Manage how you sign in to Microsoft (live.com) to set a new alias. (If the system asks you to do this, log in to your MS account.) You can set your login preferences below, uncheck the box of your previous alias so that other users can't try to access your account through your previous alias.

Additionally, you can enhance your account security by adding new security information, please note that if you have double authentication turned on, it is a good idea to add more than 3 possible authentication methods
You can refer to the following links to improve the security of your account:
How to help keep your Microsoft account safe and secure - Microsoft Support
I hope the above information can help you!
Feel free to write back if you need more help.
Best Regards,
Icon - MSFT | Microsoft Community Support Specialist