SSL certificate for website - no legal company name?

Solution 1:

I just used my domain name as the Organization name. They'll usually accept that.

Solution 2:

the Organisation name doesnt have to be strictly accurate unless its organisation validated, for basic domain validation certificates, they only validate that you do indeed have control of the domain, any value will work in the organisation field in this case, its generally simplest to use the domain as @bahamat says or make up an organisation name or even use your own name again

on a domain validated certificate the organisation that you entered in the CSR generally is never shown