Here's an open source alternative you can self-host: https://llmgateway.io/

I think it's just called OpenRouter because the founder previously started OpenSea (an NFT marketplace), and also probably to sound a bit similar to OpenAI. It's like companies calling their products "natural" or "organic" or "artisan" when they can get away with it, just a marketing strategy of using words that conjure up vaguely positive connotations in your mind.