Your feedback is appreciated. What's in a name? Sometimes a name that has no meaning is a perfect choice because it allows us and you to create its meaning. It would be hard for us to continue calling the site FreeBitcoin if we were offering more than Bitcoin. Names like "Google" or "eBay" or "Alibaba" are weird before their presence in the market builds their personality.
What's in a name? A brand name is often one of the most valuable assets a business owns. You chose some good examples there. Google has a market capitalisation of $773Bn and according to Forbes $101.8Bn of that is the value of the name alone. All those companies spent an absolute fortune on marketing to build up brand awareness and they wouldn't throw that away. Companies only usually rebrand after bad publicity to try and disassociate themselves from their own past. Given the fantastic reputation, Freebitco.in has it would IMHO be a mistake to chuck that asset away.
I'd also agree with @LTU_btc. Outside of the crypto world the mainstream media is just starting to pay serious attention to Bitcoin but very few have heard of altcoins. The name Bitcoin in itself has a massive brand value.
It's your business to do as you please but I think this is a poor decision from a business perspective.