My thoughts are similar. Think about the name “Republican” and strip away the negative connotation it now has with most of us. A party favoring a Republic, a nation of law (the Constitution), not on majority rule (Democracy; Democrats).
So the problem isn’t the name of the party or what it should stand for based on its name. The problem is it’s been overrun with people who don’t value the Constitution and the limited government principles contained therein. We need to work within the party to make the Republican party stand for what it should literally - a free Republic.
Here is why Third parties never take hold in the US-—unlike Europe. In Europe they have parliamentary governments and elections. You might have three or four conservative parties and two or three left wing parties. After the election is over, whichever coalition is the biggest can get together and elected a prime minister and coalition cabinet and government.
Here in the US it does not work that way. We have a winner take all type of election system. Say you have a particular congressional district that leans conservative. In a congressional election, the Republican and Third Party Conservative candidate split between them 60% of the vote. The Democrat, however, wins 40% of the vote. Even though the district voted 60% conservative, the Democrat wins. This is why third parties never take hold in the US. And never will.