Image: NEO discoveries by year by survey. CSS is green and PS is purple.
NEOs are discovered by imaging an area of the sky 4 times over about 30 minutes (CSS and PS). When you do a time spaced series like this objects like stars do not move. Anything that is moving is going to be in near-Earth space or orbiting around the sun somewhere in the solar system. These images are sent through complex computer pipelines that reduce the data, remove static objects, and detect moving objects. These moving object detections are mostly false - hot pixels, cosmic rays, flat artifacts, ect, so a human will typically verify the detection is a real object. After an object is determined to be real and new it is sent to the Minor Planet Center (MPC) for publishing. The MPC is like the clearing house for astrometric observations of asteroids and comets. Their data is populated out to institutions across the globe. NASA's JPL uses this data to monitor for potential impacts on its public facing site Sentry. MPC publishes data on new objects within a few minutes of receiving it, and data on known NEOs once a day. The European Space Agency also keeps its own impact risk list here.
You can see on the JPL Sentry page that an newly found asteroid (2022 AE1) currently holds the top spot for a potential impact (1/1700 odds) in July 2023. Nothing secretive happening here. This impact will mostly likely be ruled out as the orbit is refined more via more astrometric measurements in coming weeks.
It is imperative after discovering a new NEO to get it published to public facing websites ASAP. The primary reason is you cannot resolve the orbit of an object that only has 20-30 minutes of observations on it to any degree of confidence. Basically, we don't know where the objects are going after we find them, they must be tracked. The main reason for this is we only have a tiny sample of its orbit and there are astrometric uncertainties with the observations. Observations of asteroids are not perfect. There are tiny errors usually on the order of less than 1 arcsecond per observation that affect the orbit solve. If you only have 30 minutes of observations of a new NEO, and you don't continue to track it, the number of orbits that fit those observations will eventually span the entire night sky after a few hours/days. These rocks can and do get lost because of this. Large long period comets are often found while they are still well out past Jupiter. These objects are moving very slow and they are fuzzy which makes them even harder to measure and increases the number of possible orbits that fit the observations. It can take well over a week to have a really good idea of where one of these new comets is headed once it's discovered. This is one area where professional astronomy relies on amateur astronomers a lot. There are amateur astronomers across the globe that help track these new discoveries often from their back yards with telescopes in the 10-14 inch range. They are able to do this because all of the data is published by MPC in near real time. Without this data being made public quickly, we'd lose more rocks than we find and we'd have no clue where they were going.