The two wings of the Democratic Party control the two major political organizations as machines. The left-wing Democrats run one under the "Democratic" brand. The right-wing Democrats run the other under the "Republican" brand.
The Republican Party has opposed political machines. Their ideological action is primarily through civic improvement. Republicans tend to be volunteered for office, but will occasionally run if they feel called to bring reforms. Their motto is from National/Whig Republican Henry Clay:
"I would rather be right than President".
But how did their political organization fall into Democratic hands?
In the early 1960's, Right-wing Democrats took a look at the mostly moribund political organization from the Fremont and Lincoln days, seeing an opportunity, a shell for their hermit-crab democracy. They were referred to by Nelson Rockefeller in the 1964 Convention as anti-Republican: "These people have nothing to do with Americanism. The Republican Party must repudiate these people." [Note: "Americanism" means "American Republicanism".]
Party chairs,who had previously begged Republicans to be volunteered for the nomination, suddenly had a new problem: Right-Wing Democratic politicians getting other Right-Wing Democrats to register as "Republicans" and to sign their nomination petitions. Over the past half-century, more and more Right-Wing Democrats have used elections to gain positions of power as "Republicans". They have, however, retained a distaste for the name "Republican", preferring to call themselves "Conservatives", as in "Conservative Democrat". One might say that they are "crypto-Democrats".
Yet they find the "Republican" name useful. The Left-Wing Democrats can slander Republicans with every attack they would make against the Right-Wing Democrats; they can, they do and they relish doing that. Then the Right-Wing Democrats can appear pure as "Conservatives", even maligning Republicans as "Establishment Republicans". It is great fun for the Democrats to vilify Republicans from both sides, inside and outside.
What I am proposing in my candidacy, besides the usual stock-in-trade of Republican reformers, is to restore the good name of the Republican Party. I may not become President, but I will certainly be Republican. My fellow Republicans deserve nothing less after decades of hate-mongering against us and our party.