Whether or not you use the same name for your eCommerce store and brick-and-mortar store(s) will depend on a number of factors including how well-known your offline brand is, how SEO-friendly your name is, etc.
There can be a lot of value in keeping the same name if a lot of people know it and associate it with your industry. However, if your name isn’t well known and doesn’t immediately draw a connection to what you sell, then you might want to choose a name that is more likely to capture search traffic.