A trademark includes almost anything that is used by a person or entity to identify a product or service. This includes product names, company names, logos, slogans, service names, slogans, taglines, colors, product packaging, product shapes, symbols, sounds, fragrances, flavors, and domain names. A trademark functions to identify and distinguish goods and services from those manufactured, sold, or provided by others and to indicate the source of the goods or services, even if the source is unknown. Trademark registrations can be renewed forever as long as they are being used with the corresponding goods or services in commerce.
A partnership firm can be registered whether at the time of its formation or even subsequently. You need to file an application with the Registrar of Firms of the area in which your business is located.