The White House doesn't want the GOP Obamacare replacement branded 'Trumpcare'

President Donald Trump's administration, its media boosters, and its critics are playing a game of nickname hot potato with the Republican bill to repeal and replace Obamacare.

Much like Republicans shifted the conversation to dub Democrats' healthcare overhaul "Obamacare," opponents of the American Health Care Act are trying to pin the bill on a single politician.

The only difference with the AHCA is that there are now two alternatives being thrown out: "Trumpcare" and "Ryancare."

Trumpcare seems to be the tag of choice for many Democrats. Senate Minority Leader Chuck Schumer called the bill "Trumpcare" on the Senate floor Tuesday.

The Trump team, however, has pushed back on the name. White House spokesperson Kellyanne Conway pushed for the use of the official name instead of "Trumpcare" during an interview with Fox News on Wednesday.

"I'll call it Trumpcare if you want to, but I didn't hear President Trump say to any of us, 'Hey, I want my name on that,'" Conway said. "We're happy it is the American Health Care Act. This is serious stuff. This isn't branding according to someone's name."

Secretary of Health and Human Services Tom Price also deferred when asked whether he would call the bill "Trumpcare" at a White House press briefing on Tuesday, saying he would "let others provide a description for it" and that he liked "Patientcare" better.

After his administration discouraged it through much of his first term, President Barack Obama embraced the name Obamacare as far back as 2011, saying it showed he cared about Americans. (Polls have shown Americans dislike the ACA much more when it is called "Obamacare" rather than the "Affordable Care Act," however.)

The American Health Care Act's other emerging nickname, "Ryancare" - a nod to House Speaker Paul Ryan - has popped up in a diverse group of places.

Right-leaning websites, including Breitbart, have pinned the "Ryancare" label on the AHCA because of reasons stemming from discontent - they do not think the bill goes far enough in repealing Obamacare.

At the same time, left-leaning websites like the Daily Kos and Daily Beast have used the "Ryancare" moniker to attack the law for going too far and possibly leading to the loss of health coverage for millions of Americans.

The conservative group Club for Growth similarly used the moniker in its rebuke of the healthcare bill.

As the bill progresses through the House and Senate, it remains to be seen which of the names - if any - will stick.