Of course. Anyone can design their own logo. Most businesses start off this way, using tools like Canva, Fiver and logo generators to create free/cheap logos.
But one, question I would ask is how do you want your brand to be presented? If you want to be unique, using a tool like Canva or Fiver can align you with thousands of other businesses, all trying to stand out.
A logo performs a lot of tasks and needs to be easily recognised and tailored to fit your target audience.