Homebrew installs nvm but nvm can’t be found afterwards?

Did you follow the instructions listed in the caveats?

[~] brew info nvm
nvm: stable 0.20.0, HEAD
https://github.com/creationix/nvm
Not installed
From: https://github.com/Homebrew/homebrew/blob/master/Library/Formula/nvm.rb
==> Caveats
Add the following to $HOME/.bashrc, $HOME/.zshrc, or your shell's
equivalent configuration file:

  source $(brew --prefix nvm)/nvm.sh

Node installs will be lost upon upgrading nvm. Add the following above
the source line to move install location and prevent this:

  export NVM_DIR=~/.nvm

Without the extra config it doesn’t look like it will find NVM by default..