FreeForm 4.2 EE 2.8.1 MSM
Today I needed to create the first form for one of the sites on our EE with Multi-site. So I began by creating fields. I went to create a First Name field, but FreeForm told me the field name already existed and I needed to select another name. Which was a surprise to me since this was the first field and form I was creating for this site. I checked the fields list and it clearly wasn't showing. So I checked the other site and confirmed the field name was being already used. So I had to switch my field naming conventions to help differentiate. And I created all the fields needed for the form. But I didn't use a different convention for the field label.
Then I began to create the form, setting the Form Type to Composer. In the list of fields, I now have two First Name fields. The list uses the field label, so now I can't tell them apart. I have to edit one to check the field name so I select the field for this site and not the other site.
I suggest that you either let FreeForm share the fields across the multiple sites or create a better separation between the sites. And I lean towards the latter. And by better separation I think I should be able to reuse the field labels, field names, form names and form labels etc without worrying about names on other sites.