The short answer is, Impact Wrestling, owned by Anthem Media.
The longer, stupider answer is that they started off as NWA-TNA in 2002, but started phasing out the "NWA" part fairly quickly--when they started doing house shows, it was as "TNA Wrestling." Around 2010 or 2011, TNA did a confused, partial rebranding and renamed "TNA Impact" "Impact Wrestling", but the company was still TNA.
Towards the end of 2016, TNA was absolutely running out of money, getting loans by pledging ownership shares in the company, and streaming rights to the tape library. There was a legal scrum between Dixie Carter/TNA and Billy Corgan, and Anthem MEdia (who owns their Canadian TV network) provided the funds to keep operating and to pay off Billy Corgan's loans, and a bunch of other loans, but Anthem took over the company.
Anthem isn't run by complete mental defectives, so they realized that TNA was a bad name, and used "Impact Wrestling" for everything. (I don't know if there was ever an official announcement changing the name, or if they just never mentioned "TNA" and called everything "Impact Wrestling". The LOLTNA page refers to an episode where Bruce PRitchard, who was probably an on-screen authority at the time, saying "TNA IS DEAD").
In the year that Anthem has had control, they brought in Jeff JArrett and were doing a very gradual merger with Jarrett's GFW (Global Force Wrestling), whose only real asset was that their name didn't make you think of a Three's Company/Baywatch/Charlie's Angels syndicated TV block. They changed the name of the company from TNA to GFW (a couple of months of TV were built around the GFW invasion and takeover), without actually completing the process of buying the GFW trademarks.
And then they fired JEff JArrett for being drunk and erratic. Which meant they pretty much had to dump the "GFW" name and go back to being "Impact Wrestling."
So now it's Impact Wrestling. One problem is, it was both Impact WRestling and TNA for about 6 years, complicating a rebrand. Another problem is that, in the last 12 months, they've changed names 4 times, from TNA to Impact to GFW back to Impact, so people just call them TNA because they've been calling it TNA for 15 years.
Unfortunately, LOLTNA is the only identity this company has ever really had for very long.