Legislative drafting conventions are conservative, and it is traditional for a bill to have a long title which describes the purposes of the bill in technical detail, and then to include in the first section a short title which provides a more user friendly name. The short titles of Acts used to be fairly straightforward (e.g., the “Revenue Act of 1939”) but by the late 70s or early 80s, they tended to get cute and political, so now we have names like the “PATRIOT Act” and the “Affordable Care Act.”
The tax bill just passed by both houses of Congress introduces a new and somewhat unprecedented variation. There is no short title. There used to be: the “Tax Cuts and Jobs Act” (TCJA). However, at the last minute, it was stripped out of the bill because the Senate Parliamentarian ruled that it was extraneous to the bill’s purpose of affecting revenues, which is what a reconciliation bill is limited to. Hard to argue with that – the name of the law does not have an effect on revenues.
As a result, it would not be accurate to refer to this piece of legislation as the TCJA. Opponents have been referring to it as the Trump Tax Scam, and likely will continue to do so. It is probably too much to ask the media and tax advisors to refer to it that way, since that does seem overtly political. The “2017 Budget Reconciliation Act” perhaps would work (BRA for short). Several pieces of legislation enacted through reconciliation procedure have been called “Omnibus Budget Reconciliation Act of 19xx” so there is precedent. So calling it a Budget Reconciliation Act is a correct generic description in the absence of an official short title. I believe that calling it a tax reform act would also be political, since it falls far short of reform. Budget reconciliation is perhaps as neutral as one can get. An additional argument for this is that the bill contains not only tax provisions but also provisions on Alaska drilling, which are not tax related, but are related to budget reconciliation.