Their is two types of Bitcoin core, so the later needs to change the name

[Bitcoinpro]

one referes to the core software needed for a Bitcoin client

the other refers to a team of people with a proposed set of

updates/timelines/ideas as opposed to another group

called classic with different values,

the name core is already taken so this proposed

core altcoin needs to change its name

[Jeremycoin]

I think it's not that necessary, because people will understand what it's refers to based on the topic that they're talking about.
Just like when you talking about the Blockchain(Wallet) which can refers to Blockchain(system), if the topic is about a Bitcoin wallet then the "Blockchain" is a wallet.

[unamis76]

There is only one Bitcoin Core. Core and Classic are two different clients. No one is trying to compete for names and both are proposals for a set of rules in Bitcoin. There is no "core altcoin". I don't see any confusion here