The two political parties in this country are the Insiders and the Outsiders, one believes in growing government and the other believes in shrinking it. The Democrats and the RINOs are the Insiders and anyone who works for more Liberty and personal freedom is an Outsider.
Marco Rubio has been told by Shumer that his political future depends on toeing the Insider line if he wants to stay. Ted Cruz has been told by McCain he doesn't understand how things get done but he continues to represent the people who sent him to the Senate anyway.
Just like the Progressives took over the Democratic party the Tea Party can return the Republican Party to the people so no need to change the name.