If you are a British citizen, you probably can obtain a coat of arms. An article in the Mirror web site at http://www.mirror.co.uk/news/ampp3d/missed-out-new-years-honours-4897332 will help you find out if you’re eligible.
Citizens of other countries also might be eligible for a coat of arms but the article in the Mirror only covers Great Britain. However, you cannot claim a coat of arms as your own simply because someone else of the same last name had a legitimate coat of arms. In most cases, each individual must obtain his own, personal coat of arms. In most cases, there is no such thing as a “family coat of arms.”