Their cli commands generic, but their product name has always been distinct. It has always been Visual Studio Code and now Visual Studio Code Server. VS Code, VS code server for short.
Your branding, "coder" and "code-server", is just super generic and popular terms. That's what makes it hard to search for, not the cli command names.
Perhaps since public release, but I was informed by a PM who was part of the original product development that this was a concession to marketing, and it did not always have the name “visual studio” attached.
Which is exactly OPs point. If they’d brought it forth with just the name “code” it would have been just as dumb as these guys complaining about code-server. Which is exactly why it ended up vscode, which is destiny enough that it possible both to market, distinguish and protect as a brand.
Worth mentioning that gitpod's openvscode-server is a third option. I prefer it to code-server since gitpod's has proper parity with a desktop vscode install, while coder's implementation fails to work with several plugins when loading them in manually
Your branding, "coder" and "code-server", is just super generic and popular terms. That's what makes it hard to search for, not the cli command names.