Thanks for all replies guys. I owned you some update on this.
First when I've renamed the server I didn't think about unticking B2B.
When I've deleted two tasks from Scheduled Task, the box was still ticked in B2B.
When I was trying to untick and tick again, the save button was greyed out as the system knew that I didn't make any changes. So I put space at the end of the task name to have save button enabled.
After I saved it, two new task have appeared in the scheduled tasks, however when I was trying to open them I got initialization error, so couldn't edit them. I noticed that it still creates the task with old server name, so thought that this is why I got the task initialization error.
The solution to prevent this error in Scheduled Task from happening, was that I should untick the box in the SIMS then save it, then tick it again, and then save it again. Very simple, but cost me so much hassle. I have no idea why I didn't think of this in first place.
This way I was able to edit both B2B tasks, which were STILL having old server name, and put new server name into it.
I noticed then, that files have been successfully generated, however I was still having problem with File Posting: Failed status in the B2B log, but this was due to the proxy setting change. After removing proxy from configuration Files have been successfully posted.
One problem still exist: running solus to check the updates still gives me login error reason 6, even after detaching and restoring database and regardless of proxy settings.
Conclusion:
My original question is still valid where SIMS keeps the server name for those scheduled tasks (maybe this is only within SIMS tasks, however I don't know how to edit them within SIMS)?
Even If I could correct this old server name in tasks within SIMS, I would still have to do this ticking and unticking, to solve the problem.
I think very important thing is fact that modifying server name in b2b windows task is SAFE and will do the job.