Planning on rebranding! How should I go about it?

Hi,

I have a business account on SS and my website URL is www.businessABC.com, I want to change it to www.myname.com.

That would not be a problem and from what I know I would just need to buy a new domain and set it as my primary domain.

My main problem is with G Suite. When I signed up to SS I got G Suite 1st year for free and I have been using it as my main business email account. Ideally, I was planning on keeping the old domain for the website as a transition phase for a few months. Since I would only need to pay an extra 20$ for the domain, it would not be a huge problem. But the G Suite is around 80$, so to keep the old email address I would have to pay the 80$, plus an extra 80$ for the new email after rebranding. Things are getting a bit expensive.

Are there any alternatives? How would you go about it?I have a few business relationships built on that email and I was wondering what happens to it if I don't renew it. I can forward everything to other email account but what would happen if someone sends an email to the old email address?

I was thinking if it would be possible to transfer the domain I have on SS to GoDaddy or BlueHost, maybe get some hosting there and continue running the email account from there... But I have no idea if that is a possibility.

I must add that I'm right at the end of my first year in SS. So everything is about to renew, hence my dilemma.

Thank you in advance,And feel free to ask me any question, if you need any information