A logo mark is a commonly used term for a figurative trademark and consists of a graphical element or figure. A figurate or logo mark can be just the figure on its own, or it can be combined with one or more words. Words in a specific font are also considered figurative.
A word mark gives stronger rights to the use of the word, which is usually the most distinctive and identifiable element of a trademark. However, if the word mark cannot be registered due to lack if distinctiveness or similarity a figurative (logo) version may succeed by being distinctive and easier to defend against objections and oppositions.
You can trademark a brand or product name. Or a figurative mark which is the legal name for a logo. As long as they are distinctive and not too similar to existing trademarks that are registered or widely used. Other things that can also be trademarked, though these are less common such as sound, pattern colours either singly or in combination, holograms, multimedia and motion. Smells have also been trademarked.
What can not be trademarked varies between registries. All require a trademark to be distinctive and not too similar to other trademarks for similar Goods and Services. Also they can’t be offensive, such as swear words or pornographic images. Or be desciptive and commonly used words or language that should be free to use, or too common or bland,, such as ‘the leading firm’. Lastly a trademark cann ot be too similar to state symbols like flags or hallmarks.
A common law trademark is one where rights are established through widespread use over a number of years. And without registered rights being secured through the relevant registry. Common law rights are equal to registered rights, but harder to prove, and the cost of doing so will normally be many times the cost of registration. It is unwise to rely on common law rights and no established brand owners do.