Install Docker Desktop via brew
$ brew install --cask docker
Dont’ forget add --cask option since there’re formula and cask for docker.
After the installation, you can see ✔ mark next to Formulae docker and Casks docker.
$ brew search docker
==> Formulae
docker ✔ docker-compose-completion docker-ls docker-machine-driver-vmware docker-machine-parallels docker2aci
docker-clean docker-credential-helper docker-machine docker-machine-driver-vultr docker-slim dockerize
docker-completion docker-credential-helper-ecr docker-machine-completion docker-machine-driver-xhyve docker-squash lazydocker
docker-compose docker-gen docker-machine-driver-hyperkit docker-machine-nfs docker-swarm mockery
==> Casks
docker-edge docker ✔ docker-toolbox
Reference
macos - Brew install docker does not include docker engine? - Stack Overflow