Is this a mistake or just phishing?

I guess the first question is, did you add a recovery contact?

Refer to:L Help a friend or family member as their account recovery contact - Apple Support

1. Go to Settings

2. Select Password & Security

3. Select Account Recovery or Recovery Assistance

Is there a strange name there?

Scams (e-mail, text messages, and phone calls) are getting very good at closely imitating true Apple communications. Always be cautious. Here are some guidelines:

Identifying legitimate emails from the App Store and iTunes Store - Identify legitimate emails from the App Store or iTunes Store - Apple Support

Recognize and avoid phishing messages, phony support calls, and other scams - Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support

Avoid scams when you use Apple Cash --> Avoid scams when you use Apple Cash - Apple Support

Apple 'How to identify, avoid, and report phishing' video--> https://youtu.be/SR3Z3fXXjfw

If you are uncertain about a message and a resource provided in that message, do not click on any links in the message. Try to independently verify the resource by going to a support page on apple.com and use that to contact Apple or to use the service the message is telling you to use.