It’s very important to claim your business and verify it with Google – not doing so could potentially result in your business listing being ‘hijacked’ by a spammer or competitor, with disastrous results for your reputation. At the very least, you could easily end up with wrong or misleading information being shown to your customers.
To change your address, or any other details on Google maps, you first need to claim and verify your business with Google.
Log into your Google account with your Gmail email address and find your business listing on Google, then click ‘Own this business?’.
Then follow the instructions (- there’s more detailed info here: https://support.google.com/business/answer/7107242 )
If you are a local business with a physical address, choose to verify by post – Google will send you a postcard with a code. You may not be able to verify any other way.
It’s all a bit long winded, but the process helps to make sure it’s secure, and no-one else can steal your business listing – just go through the steps methodically.