To me, the IDENTITY / IMAGE is the foundation of any business. Identity can be first concretized through the NAME of the business. Before you can actually get started the name should be legalized and approved by the country's Department of Trade and Industry. There are laws out there that one must comply with before one can start using the name in public. The Philippine Law governing the registration of a business name is Act No 3883.
With regards to coming up with the name. One can start by brainstorming words that are catchy or words that facilitate recall. Some people use tools to come up with a unique brand/name. One can come up with a list which can later on be narrowed down into the top options. One can make use of a word map. Allowing one word to branch out into other related words. There is no wrong idea during the brainstorming process. Just keep writing and let the ideas flow. Some focus on the product/service and think of words that would best capture that. Some would tweek the spelling or consider synonyms and antonyms. Some would factor in cultural expressions. A good way would be to place oneself in the shoes of the customer/client/target market then start questioning the overall impact of the name though of: Will I remember the name when I see it once? What does the name remind me of? Does it give a good first impression? Are there existing names already out there that are similar? Is the name easy to remember/spell?
Once you've come up with your top 3 name choices, check whether that name has already been taken in your country/municipality/province.
For the Philippines: https://www.bnrs.dti.gov.ph/web/guest/search
If the name is taken or if there's a similar name already existing, try brainstorming again. Chances are it would get denied. It costs P300 to register a name for sole proprietorship. So as much as possible one would want it to be a success during the first try.
Basically, the challenge is to come up with a name that other people have not thought of yet. The process is actually fun. Some people even enjoy doing the process with friends. You'll be surprised with the tons of ideas that can simply keep flowing.