EnterraHost
If you already own the domain, and especially if you already run a website on it, sending business mail from a free address is the one place where the two halves stop matching. The website says you are a business. The email address says you are somebody with a laptop.
What the address actually tells a customer
Nobody reads an email address and consciously evaluates it. That is the point. It is read in a fraction of a second along with the name, the subject line and the formatting, and it lands as an impression rather than a judgment.
An address at your own domain reads as a business that has set itself up. A free address reads as either brand new, or not serious, or working from a kitchen table, and the reader has no way to tell which. The information they wanted was whether to trust the message, and the address is part of what they used to decide.
The effect is strongest precisely where it matters most. A quote, an invoice, a contract, a first contact after somebody has looked at your site. Those are the moments a mismatched address costs something, and it is not recoverable later in the same thread.
The practical problems are worse than the impression
Trust is the soft argument. There are harder ones.
A free mailbox is not yours. It can be closed, suspended, rate-limited, or changed in ways you do not control, and none of that requires your agreement. If that address is how customers reach you, you have built your inbound channel on somebody else's terms, and the recovery path is whatever they decide to offer.
It also cannot be transferred. A business that sells, or a person who leaves, cannot hand over a free address the way they can hand over a mailbox on a domain the business owns. The correspondence and the identity are stuck to an individual.
And it does not survive having a website. Once you are paying for a domain and a site, the mail is the cheapest part of looking like a real business, and leaving it on a free service means the one thing every customer sees is the one thing you did not set up.
What actually changes when you move
Less than people fear. The address you send from has your domain after the @, and everything else about using mail stays the same. Same phone, same desktop client, same habits.
You are not abandoning the old address either. Mail sent to it can be forwarded so nothing is missed during the change, and you can keep it as a second address for personal correspondence while the business runs on the domain. Moving your existing mail across covers bringing the history with you rather than starting empty.
The part that is not optional
One thing does have to be done properly, and it is the reason some people try this and conclude it does not work.
Sending from your own domain means the receiving server checks whether your domain authorised the message. That is what SPF and DKIM records do, and without them a perfectly legitimate email looks to the other end exactly like somebody forging your address. It lands in spam, or it is refused.
This is not a switch you can skip because mail technically sends. It is the difference between sending and arriving, and adding SPF, DKIM and DMARC is the job that makes your mail land. Set it up before you send anything that matters.
What to do first
Mail needs a domain, so if you do not have one yet that is the first step and registering a domain covers it. If you already have the domain and a website on it, you are one mailbox away from the two matching.
If you are moving an existing address rather than starting fresh, moving your mail from Google Workspace and the other provider guides cover the move itself, and the business email page has the prices.