I ask because DC Extended Universe was trademarked and various magazines and websites refer to the DC films in development as the DCEU, but that new DC special was called DC Films Presents and the newly official DC movie page is called DC Films.
It was never actually trademarked. You can do a TESS search. The journalist added it to give the name an air of authority when it has never been on a single Warner Brothers product, never been directly uttered by a single brain trust member in quotes, has never been promoted or pushed by the WB, and simply isn't official. Some fans latched on to it too early and now won't let go despite all evidence to the contrary.
Does it need an official universe name?
No, but it's useful to control your branding and licensing, especially if you have similar products. The WB also has the Arrow-Flash continuity, so "Justice League Universe" separates it from: a) non-film TV products; and b) non-continuity DC movies like Sandman.
The X-Men film universe has nothing to separate itself from so it doesn't need a name.
Never. You will not find a single WB press release, official WB product, repeated quotes from braintrust mouths, a single dollar spent pushing "extended", or even one-iota of effort to claim "extended" on social media by Warner Brothers.
However, "DC Films" and "Justice League Universe" are in a press release, on official WB products, come directly from Roven and Johns, cost at least a million dollars to put that message out, and the WB has claimed sites tied to the two.
We do not
know either way whether "DC Films" is an entity or not. Corporate restructuring is second-nature to the WB at this point (they restructured for DC Entertainment, before Tsujihara, and again once he became CEO). Even if it isn't a legal entity, it still acts as branding for the braintrust that's overseeing the cinematic exploitation of DC intellectual property. Literally being a subsidiary studio within WB is kind of irrelevant at that point.
We don't
know that "Justice League Universe" excludes Sandman or Shazam, but we do know that it includes everything talked about in the special- MOS, BvS, SS, WW, JL, Aquaman, Flash, & GLC. It is extremely convenient to have an official brand to talk about all the films common to that one continuity and since 8 out of 9 films (JL has two parts) are all Justice League films (and SS still takes place in the same continuity and features Batman with a Superman name drop), it's a completely reasonable name to use.
Lots of franchises never get to 9 films and still have a brand name for all the films... "Justice League Universe" makes sense for these 9 (11 if you count stand-alone Batman and Superman films).
Meanwhile, "extended" never made sense.