Rebranded and redirected

We just went through a rebrand and changed our domain name. Nothing was done to prepare from an SEO perspective other than redirect the old domain to the new one. I asked for access to Google analytics for the new domain but was told that nothing changed with the domain change. So in GA I'm seeing traffic but that's because we're marketing our rebrand. I'm worried about organic traffic over time. Am I worried for nothing? Simply redirecting to the new domain doesn't sound right to me but I'm not an expert. Will I see a negative impact to organic traffic because of how this was done?