Interestingly, we’ve successfully resolved Betelgeuse as a disk.
Not as accurately, but there are other methods. Such as redshift - the farther away an object, the greater the redshift. And there’s several other methods, like using particular types of stars as “standard candles” that have a predictable brightness at a given distance.
We’ve also actually checked. We’ve had several probes further out (in some cases much, much further out) than the OP’s conjectured distance take pictures back toward Earth. No stars showed up that weren’t supposed to be there, nor did the probes pass by any they felt like photographing, reporting, or adjusting course to account for the gravity of.
This. All knowledge is contextual. You can’t change a fact of nature without changing a lot of other things. The distances to the stars rely on quite a few other facts we know about the universe, and those facts are related to quite a few other facts. If you think stars are that close, you’ve got to back up that claim with some very fundamental physics.
I understand how astronomers find out how far away the stars are, and how big and how bright, and even how old they are, but how do they find out their names?
Stellar distances are typically estimated by evaluating luminosity and spectral content (the characterisic distribution of wavelenghts of visible, infrared, and ultraviolet light from a star) which determines the composition and stage of life of a star. By knowing what the brigtness of a star should be at some reference distance, astronomers can estimate the distance (and by measuring the frequency shift, the radial speed) of a star with respect to an Earth reference frame. At farther (galactic and beyond) distances, objects such as Cepheid variables which are of known luminosity (referred to as “standard candles” in astronomy jargon) are used as to estimate distances and speeds, as well as the metric expansion of space as indicated by the “red shift” observed by Slipher, Keeler, and Campbell and calculated by Hubble and Humeson.
Formerly, they called Information. Now they just look them up on Facebook.
Stranger
One way that might work is if the solar system were inside something similar to a black hole, our sun might be a a reversed time image of it’s former self and time in our ‘bubble’ runs backwards, that ‘bubble of space’ could have it’s own laws of physics including the speed of light, and there is a limit as to how far light could travel, this we observe as the expansion of the universe.
But this would only bring stars to the distance of just outside the solar system, not close to the moon. But with the speed limit lifted and new laws of physics in play the stars may be easier to get to.
Are you sure about that? I thought they were named by the International Star Registry. 
Interestingly enough, in the early days of astronomy there was a legitimate debate over star distances due to an apparent conflict between star brightness and parallax. Copernicus had explained the lack of noticeable parallax by saying the stars were extremely far away. But to the naked eye and early telescopes, the stars appeared to have a small but discernible angular size due to an optical illusion. If they were as far away as Copernicus claimed, they’d have to be gigantic- as big as our entire solar system. This led for awhile to the Tychonic system, which was a compromise between the Ptolemaic and Copernican systems.