Hi keren tsur,
According to your description, I wonder if you want to use a managed property as a refiner to show the site collection name.
In my environment, the mapping of site managed property is empty. In other words, there are no crawled properties mapped to it. You could not use it as a solution.
I have viewed all the crawled properties. However, I could not find a crawled property that used to record the site collection name. There is only a managed property called SPSiteURL. The SPSiteURL managed property has been mapped with a crawled property
which records the site collection URL instead of name. You could use it directly if in need.
By the way, you can try to create a custom display template mapping the URLs to friendly names.
You could refer to the same problem below
http://sharepoint.stackexchange.com/questions/93492/managed-crawled-property-for-site-collection-title
Best Regards,