This is my solution:
- boot into the recovery mode
- open terminal
- type: csrutil disable
- press enter
- type: mount -uw / /dev/diskXsY <--
Attention!!! X=your Big Sur disk from 'diskutil list'
Y=your Big Sur disk slice
Now the Big Sur volume should be writable
6. Reboot normaly
7. name your own grafic image as Big Sur Graphic.heic
8. copy your own grafic image in to Macintosh HD
9. reboot into the recovery mode
10. open terminal
11. type: mount -uw / /dev/diskXsY <--
Attention!!!! X=your Big Sur disk from 'diskutil list'
Y=your Big Sur disk slice
12. type: cd /
13. type: cd /Volumes/Macintosh\ HD/System/Library/Desktop\ Pictures
14. type: mv /Volumes/Macintosh\ HD/System/Library/Desktop\ Pictures/Big\ Sur\ Graphic.heic /Volumes/Macintosh\ HD/System/Library/Desktop\ Pictures/Big\ Sur\ Graphic.heic.orig
15. type: mv /Volumes/Macintosh\ HD/Big\ Sur\ Graphic.heic /Volumes/Macintosh\ HD/System/Library/Desktop\ Pictures/Big\ Sur\ Graphic.heic
16. Reboot
Now you have your new login background
17. Reboot into the recovery mode
18. open terminal
19. type: csrutil enable
20. press enter
21. reboot e voilá
¯\_(ツ)_/¯