When you installed it, it put a file named homebrew.mxcl.memcached.plist in /usr/local/Cellar/memcached/$version/; you copy that file into ~/Library/LaunchAgents and then tell launchd to start it with launchctl load -w ~/Library/LaunchAgents/homebrew.mxcl.memcached.plist.
If you were watching the console carefully during the brew install command, it should have said something about doing these exact steps. If you run brew info it’ll re-print this information, e.g. brew info memcached.
You should probably read https://docs.brew.sh/Manpage — it has more useful documentation including the brew remove command which will remove the package if you decide you don’t want it.