Trademark registration is completely optional in the USA, UK and some other countries. When you are the first to USE a distinctive brand on particular goods or services in commerce, you automatically become the owner of enforceable rights in that trademark for those and similar goods and services in your field.
You may optionally register in one or more states or in the USPTO.
However, your question also carries the issue of whether you can "name" something new with a trademark, which is a brand. The answer is: Not for very long. As soon as your brand becomes the "generic" name for your product or services, it is no longer a trademark, having suffered "genericide".
For instance, escalator, kerosene, thermos were once valuable trademarks, when used as adjectives.
Once they became nouns, they began to lose all trademark value. Similarly if you use it as a verb, as in "go xerox this for me". Xerox is a brand, not a noun or a verb.
Therefore, you would need a plan with a description of your new subcategory and a completely separate 'brand" for your particular goods or services withing that new subcategory, if you want a trademark.