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Hi Ali! I like Ryan's thinking and also want to emphasize one important point. Just because the new homepage will be beautiful, doesn't mean it can't include any text. There should still be crawlable text on the homepage, meaning you can still talk about your service there. Don't do away with all text.

Start using the DFP ad server and target the ads geographically. When someone in your service area lands on the page, do not show the ads or show a house ad. When someone outside of your service area arrives, then show them the ads.  Adsense will target by contextual relevance, geographic area, behavior, remarketing, etc to give those people valuable ads. Sell that ad space by geographic area to people in your industry who serve other areas.

Hi Ali, So, Google's guideline on this is that the business name should be exactly what it is in the real world (https://support.google.com/business/answer/3038177?hl=en_). Businesses should not be adding modifiers to their name for the sake of search. If the business is now considering going through a formal/legal re-branding process, then this would be mean marketing-wide, including the website, all citations and other web references, the way the phone is answered, print materials, radio and TV advertising. You'll need to pick one name and use it everywhere. This will need to be the legal name or DBA. Yes, it could be of some degree of help if the legal business name included the city in it, but whether this advantage would be great enough to warrant the major task of a formal re-brand will be a big decision for the company to make.