It's really just about what markets well. Come up with a catchy name and that name will stick.

The Democrats didn't go far enough accepting the Obamacare name. Obama was all 'sounds good to me, yes, I care' or something along those lines when he was asked once, but the Democrats should have officially renamed the bill to Obamacare. Because there's people who support the ACA but are against Obamacare and don't realize they're the same thing. If they'd changed the name there would only be Obamacare and a few of those people, a very slim amount, might realize that the bill thats helping them is Obamacare.