Can I trademark a word, name, phrase, or logo if a different brand or business is already using the same word, name, phrase, or logo?

Yes, but it depends. When you register a trademark, you are given exclusive ownership rights to the trademark in connection with the specific goods and services listed in the trademark registration. You are not given exclusive ownership rights to the trademark for goods and services not listed in the trademark registration. For example, McDonald’s owns the “I’m lovin’ it” trademark in connection with restaurants. For example, if you are a dentist, you might be able to trademark the phrase “I’m lovin’ it” for dental services (assuming no one else has already done so).