Do I need a physical address for a Google Business Profile?

No. If you travel to your customers, Google lets you register as a service-area business, and you hide your address while still showing the towns you cover.

How to set up a Google Business Profile without an address

Set the profile up as a service-area business: list the towns and areas you cover and leave the address hidden. This is the same thing people mean by listing a business on Google My Business with no physical address. Most plumbers, roofers, HVAC companies and landscapers should be set up exactly that way. You still have to give Google a real address during verification, but it does not get published.

Using a home address, PO box or virtual office

Two things trip contractors up here. Using a home address and leaving it visible is the first, since it publishes where you live and does not help you rank. Renting a mailbox or a virtual office to fake a location in a town you want to rank in is the second, and it is a fast way to get the profile suspended. Set the service area to the places you genuinely drive to. More on getting the profile right in how to optimize a Google Business Profile.

If you are setting up a new handyman or trade business from home, see how to start a handyman business.