That’s very interesting! Around me, we called them CD Players, it must be a regional thing. Many people called the portable cassette player a Walkman, even though that was a lineup of products from Sony.

Looking on US Amazon, there are several players that have Discman, Walkman, or both in the titles. Sony must not be enforcing their trademarks (wrong term?) for the first non-sponsored listing being called:

2000mAh Rechargeable Discman CD Player:Walkman CD Player…