My usename is “cosmo”, but in the terminal konsole always is there: “-ms7d14”. For root user also is there. What is the solution for this little trouble?
What’s after the @ is the hostname of your computer (chosen during the installation)
You can change the prompt if you want (BASH):
Is it necessary for the “hostname” to be there, and is it possible for the “user” to be without it in the “Konsole terminal”? Or, to simplify… how I can change the “hostname”?
I have successfully done that, but now when I access with root, the problem is the same. My question is is it safe to make bashrc file with the same data, because on the /root/bashrc. file is empty!?

It is safe.
If you have a feeling you might mess something up, just backup your root’s .bashrc with the command cp .bashrc .bashrc.bak (when logged as root).
Then, append the line PS1='[\u]\$ ’ to your root’s .bashrc file, save, reload the shell and you’re good to go!
