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 the Affordable Care Act.

Much as Republicans shifted the conversation to dub Democrats' healthcare overhaul "Obamacare," opponents of the newly proposed 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 counselor 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 at a White House press briefing on Tuesday when asked whether he would call the bill Trumpcare, saying he would "let others provide a description for it" and 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, however, have shown Americans dislike the ACA much more when it is called Obamacare than when it is called the Affordable Care Act.)

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 News, have pinned the Ryancare label on the AHCA out of 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 The 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 the Senate, it remains to be seen which of the names — if any — will stick.