Hello stnc,
Welcome to the Apple Support Communities!
I understand that you see a badge on your Messages application positioned in the top left corner of the Home Screen that sometimes overlaps your carrier name. From your picture, it looks like the parallax affect may be making the badge from Messages appear closer to the top of your display.
I would suggest reading about the parallax affect in the attached article below and testing the feature by turning off Reduce Motion.
Reduce screen motion on your iPhone, iPad, or iPod touch - Apple Support
iOS 7 and later uses a parallax effect to create the perception of depth on your Home screen and other areas of your device. When parallax effect is on, you might notice:
- Screen zooms when you open folders or apps.
- Wallpaper icons and alerts shift slightly when you move your iPhone, iPad, or iPod touch.
- Photos or images you use as a wallpaper are slightly zoomed in or can't scale to fit the screen.
You might also see motion in apps like Weather and Messages. To reduce these types of movement, go to Settings > General > Accessibility, and turn on Reduce Motion.

Another feature that may be affecting this as well, if not the parallax effect, is the Display Zoom. If your display is zoomed in, it shows larger applications, text, and controls. Try testing with the Display Zoom set to standard as well.
Use Display Zoom on iPhone 6 and iPhone 6 Plus - Apple Support
Have a great day,
Joe