I have still used uetmplte.dat in the template directory specified in the configuration dialog. But as I now have found out this was possible only because I have never saved my environment and switched to this environment or selected one of the default environments. That's the reason why UltraEdit has still used my former Advanced menu, my customized toolbar and the template file with the old name.
So I have made a backup of my configuration files, saved my current environment and selected it. After a restart my templates are gone. But no panic, I simply copied uetmplte.dat to Personal.te1, exited UltraEdit and restarted it and my templates are back. Personal is the name I have given my environment. So now I have Personal.in1, Personal.mb1, Personal.pb1, Personal.tb1 and Personal.te1 in the directory of uedit32.ini and everything is like before.