I've never seen them used in production, people just use hex, rgb, etc.
Named colours are useful as a hint that the code might be temporary, eg. I use named colours only for debugging, so if anyone on my team sees a named colour they know something has been accidentally left in.
They're also good to inject some humour into a dry code example, eg in presentations or documentation.
An exception to the names being sourced from x11 is rebeccapurple - a tribute colour with a very specific history.