Why isn't bitcoin called bitcoin core? Or maybe another way of asking this is, if another type of node becomes the supermajority does that node type become "bitcoin"?
Bitcoin Core is the name of a software, not the name of the coin. The name of the coin should not be based on the name of the software that most nodes are running. There can and are multiple node software that enforce the exact same consensus rules and all have different names.
After all bitcoins are mined who will the power lie with (for voting on protocol changes)? I can potentially see how nodes will vote for increasing the no. of bitcoins and keeping higher fees while users would want fixed no. of bitcoins and lower fees. If >50% of nodes are one "entity" and the nodes have the power then that is far from decentralised.
There is no voting. No one votes on anything. Bitcoin is not a democracy. Even after all coins are mined, mining will still continue. No one has the power to unilaterally change Bitcoin's consensus rules. The consensus rules change when the supermajority of users, nodes, and miners all agree to change the consensus rules. Typically the consensus rules are activated when miners signal that they will be enforcing the new consensus rules. That is not a vote, it is a signal of readines.
At the moment anyone can pick their type of node/mining, but what about after all the bitcoins are mined?
There will still be mining and there will still be nodes. Mining is not just the process of generating new coins, it is the process of including transactions in blocks and that can, must, and will continue even after all Bitcoin has been mined.