Trademark registration is not obligatory, but it does grant your business the exclusive rights to a brand name or logo in connection with the goods and services you offer. It also provides you with the legal means to enforce those rights.
Whether a business should or shouldn't register a trademark depends on the nature and ambitions of the business. A locally operating hair salon may not require it, but if that same salon turned into a franchise, it would greatly benefit from a registered trademark, since a franchise is built on the goodwill and recognition its customers associate with it.
However, a business' size is not the only determining factor for obtainig a trademark. Even a single-person e-shop or Amazon store can face infringement that threatens profits and reputation. A trademark is the most effective tool for addressing those problems.