Microsoft Account Security Confirmation email

I have recently received an email on my gmail account that states:

Your Microsoft account has been renamed. We just wanted to check with you that it's okay.

     -  Old account name: my gmail account name

     -  New account name: a live.com account name not associated with me

If this is correct, you don't need to do anything.

If this is incorrect, please follow these steps:

1. Reset your password by going to https://account.live.com/password/reset

2. Rename your account by going to https://account.live.com/

Thanks,

The Microsoft account team

Shortly after that I received another email saying the account name had been changed from the new one to a completely different one at outlook.com

I am concerned first because my gmail account was listed and that is where I received the email from "Microsoft account team".  I have already changed my password on my gmail account but what other steps do I need to take to insure my accounts are safe?

Thank you!