First images from Euclid are in

What proportion of the stars in this survey have been given names (even just gibberish identifiers)? Are there too many for even astronomers to care to bother cataloguing?

Most Milky Way stars have been catalogued (to some luminosity/visibility). Wikipedia to the rescue (almost...): https://en.wikipedia.org/wiki/Star_catalogue#Gaia_catalogues

As another comment says we have a naming system for the Milky Way, but I believe the point of looking above and below the Milky Way is to explicitly find galaxies (/intergalactic forms), not stars. There’s commentary on stuff like supermassive black holes at the center of other galaxies, but AFAIK as an amateur, it’s not feasible to study individual stars in other galaxies, so we have no need to name the vast majority of them.

It’s basically impossible to grasp what looking at a hundred thousand galaxies means, and that’s just a small section. It’s literally beyond human comprehension.

  In October 2016, deep-field images from the Hubble Space Telescope suggested that there are about 2 trillion galaxies in the observable universe, or about 10 times more galaxies than previously suggested, according to the journal Nature. In an email with Live Science, lead author Christopher Conselice, a professor of astrophysics at the University of Nottingham in the United Kingdom, said there were about 100 million stars in the average galaxy. 

Which comes out around 10^24, and even that’s “likely an underestimation”. The earth’s surface area is 10^8 km^2, so naming all the stars would be like naming every spot in an imaginary grid of 0.01mm^2 (!!!) squares covering the whole earth.

Sorry for the rant, I don’t get to do any dimensional analysis in my work and miss it from HS chemistry, lol. This kinda stuff makes me want to be a flat earther…