No—if you cannot verify that you have permission, you should assume you do not have the right to use it commercially.

Images are generally protected by copyright automatically. The creator does not need to register the work, add a copyright notice, or post license terms for copyright to apply. The fact that a wallpaper is widely reposted online does not make it public domain or free for commercial use.

Using only part of the image does not automatically make it legal either. Unless the image is clearly licensed for reuse, is in the public domain, or you have permission from the copyright holder, commercial use is risky.

In practice, some infringements may only result in a takedown or cease-and-desist notice, but that risk can become much more serious if the image is used in printed materials, advertising, packaging, or other costly-to-recall work.

Safest approach: use an image only if you can confirm its license or obtain permission, or replace it with properly licensed stock or your own photo.