Catalina Photos: How do I stop the photos from moving towards me!

You can't in that view. Do the following:

1 - go to the Photos/All Photos view

2 - find the image you want to name and double click on it to enlarge

3 - type ⌘+i to bring up the Info pane

4 - click on the Add Face button

5 - resize the circle to encompass the face

6 - click on the Click to Name field and enter the name of the person:

That's it. Do it in the Photos/All Photos view.

Are you in the People view?

Is this what you're seeing:

In the People view that's what you get when you double click on a person's small image to get to the other images. It starts after a bit. Just scroll down so it's not on screen and you can then view the other pics.

Ah - ok

The eerily moving image is just a slideshow of the images below. Scroll down so it is off screen, and you don't need to worry about it. All the images it shows (that you might want to name) are in the thumbnails below.

I don't think there is any other way.

Please explain what you mean by moving towards you? If you mean the live photos playing - they'll only do that when zoomed in, and then only when you hover mouse over the Live icon top left.

I'm sorry - if it is not live photos, I have no idea what you mean by "moving towards you"