I’m using .htaccess to redirect all of my website traffic to https://www.my_domain.com from http://www.avizr.com. Should I have both properties in the Google Search Console? I guess it’s unclear to me what the purpose of having multiple properties is in the first place.
While the transition takes place, It might be interesting to keep both properties. The console will tell you if there’s any problem with the redirects (after all, it is the all Google Webmaster Tools) so you can check if there’s any traffic that, for whatever reason, is not being sent to the new site.
After the traffic reduces in the old site, you can remove it safely.
How interesting can this be? It depends on the traffic you receive. If your traffic is really low, there’s no point.