As long as you update your business information (business name, address, phone, website url) everywhere on the web, you should be okay. Your local phone number is probably the most important element of your business profile to keep consistent. If update your business name, address, or phone number (NAP), make sure you also do so on your website, your Google profile, and other directory listings. Failing to do so will result in inconsistencies in your local SEO.
Google pulls information from a variety of sources across the web. Local business listing citations should be consistent across the internet, as multiple different NAPs will give Google the impression of multiple businesses and potentially result in duplicate profiles.
To avoid all these issues when you change information or relocate, be proactive, and take control of all your local listings.