Do you give my business a domain name like mybusinessname.com?

Yes, if you select Groow PRO or Groow PRO Helper. The domain name is of your choice.
If you choose Groow BASIC then no. You will be allocated a domain that is something like mybusinessid.groow.io
When you upgrade from BASIC to PRO you will be prompted to choose a domain name or use one that you already own.