What would you call a "sheath" for a spherical object?

I immediately thought of a pouch:

noun -- a small bag or other flexible receptacle, typically carried in a pocket or attached to a belt

a tobacco pouch

I think perhaps the term cosy is appropriate. A quick Google search reveals a number of items similar to your picture which are being marketed as a "phone cosy"

For example, a red knit Phone Cosy.

Another application of the term cosy is a tea cosy

Seems to me you might be looking at a ball cosy, although it is more of a neologism than a defined word.

The term bag is used in US English for a wide variety of containers

a flexible container with an opening at one end

It also is routinely used to mean luggage and as part of the terms for specialized containers such as

• gym bag
• garbage bag
• feed bag
• punching bag
• goody bag
• laundry bag
• air sickness bag
• lunch bag

While these terms are not limited to spherical forms, they are often used to hold such objects.

An alternative is sack.

A form-fitting protective container for an object is sometimes called a shell, which ideally captures the notion of a protective covering for a round object. It usually implies a hard material, but it can be used to refer to an article of clothing intended to be the outermost layer, for protection from weather or moisture.