Moving to emojis is the next step. See huggingface.co

Oh, it's the emoji? I've just seen the domain name out and about so assumed it was Alien reference.

Same, never made the connection to the emoji myself either.

Then again, I don’t use the “hugging face” emoji almost ever. But even if I did use it, I would probably think of it visually or just as the word “hug”. That’s how I think of and use other emojis — either visually or as a simple word.

Either way, I will intentionally continue to think of huggingface.co as being a reference to Alien facehuggers.

It is their logo.

True. Still never made the connection.

Same here, though now that I think about it, a facehugger is kinda the opposite.

Maybe. But if a hugging face hugs you, it probably hugs your face. This would make the hugging face a face hugger. (But it would not necessarily make it a facehugger.)

The joke would be facehugger but maybe it could be added to Unicode.