Howto, when you applied for the software download you had to supply and email address. You should have received an email with the url for the software and a licence key.
That is targeting the English/US locale, so you may have a slightly different link, but if you go to www.sophos.com and click on the person icon on the top toward the right, you should be able to login.
Once logged in to My Sophos, choose Network Protection and then View Devices. The serial number should be showed there. I am _relatively_ sure this works for home edition as well.
If you don't have a my sophos account, CREATE ONE.
I've also figured that out. If I insert "privat" for the company name the system sends the mail with the serial number. Don't understand why I must insert a company name for privat use.