Considering you don’t have any presence on social media yet, I can’t see it being a problem to rebrand now as there is no risk of confusing your customer with the change. I think the bigger question is in these uncertain times can you afford an entire rebrand. Don’t be afraid to pay just for your basic brand elements and your logo to get something out there, and pay for the fancier stuff later. The sooner you get some presence on social media the sooner you’ll reach your customer. Go for it, just don’t worry about perfect.