Is it in general possible to calculate the loss of organic traffic while rebranding (new domain+brand name)?
Which data would you take and how would you estimate it? In which units would you calculate it?
This depends on your time, effort and methods. With a 301 redirect (if pages exists on the new domain) you pass on about 95% of your page value. Keep your oldDomain as long as viable, with a 301 header and a canonical tag.
Domain Reputation and Domain authority will reset, but, if your site is build properly, will regain quick enough. I suggest a slow transition.