Often, the main problem in such situations is poor topology. Make good topology for Text, and a thickness you need
Okidoki
Objects: Sphere, Text, Grid
Modifiers: Subdivision, Shrinkwrap, SurfaceDeform
- Create the objects and adjust the size. Text should be visually connected with Grid
- Set modifiers for Grid: Subdivision: |Simple, Level Viewport - 3| and further Shrinkwrap: by default or better |Wrap Method: Target Normal Project - Snap mode: Above Surface - Target: “None”|
- Set modifiers for Sphere: Subdivision: |Level Viewport - 3|
- Set the modifier SurfaceDeform for Text, |Target: Grid| - and click “Bind”
- Return to Grid and set target(Shrinkwrap) “Sphere”
3dnotguru, GrimZA
Objects: Sphere, Text, Circle, Lattice
Modifiers: Curve, Lattice
- Create the objects and adjust the size
- Circle shall be the same radius as a sphere and the same location
- Set modifier Curve for Text: |Curve Object: Circle|. Place it the way you want
- In Object Data Properties of Lattice, set |W: 3|, and do a size that can contains Text
- Set Lattice Modifier for Text, and choose Lattice Object
A text does not automatically adapt to a sphere, but it does not depend on a sphere
I ended up abandoning the idea of two circles because you have to pick everything up again every time. It is impossible to create an instruction. The result depends on the initial coordinates of Text and which way you turn the second circle
Jeacom
Objects: Sphere, Text
Modifiers: Subdivision, Solidfy, Weid
On the screenshot everything clear. Just say, that the result depend on Sphere Subdivision, below 3 it will be with artifacts, as in the first case
The question is not so-o-o-o-o-o-o simple
I am very grateful to you lot for answering me. If I find anything else on my own, I will add it

