Is it possible to publish one developed project under different app names by different companies?
Although it is one project, the two apps have different names and icons, and the first entry screen is also different. After that, it provides the same functionality with a few exceptions.
I would like to know if it is against the App Store policy.
There is a risk that the second app submitted will be rejected as spam.
In addition, you take the risk of account cancellation because you tried to fool the appStore.
In a word, I would not do it.
At least I would make it very clear in the comments to reviewer when submitting both apps in order to avoid account cancellation.
See Guideline 4.3:
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4.3 Spam
Don’t create multiple Bundle IDs of the same app. If your app has different versions for specific locations, sports teams, universities, etc., consider submitting a single app and provide the variations using in-app purchase. Also avoid piling on to a category that is already saturated; the App Store has enough fart, burp, flashlight, fortune telling, dating, drinking games, and Kama Sutra apps, etc. already. We will reject these apps unless they provide a unique, high-quality experience. Spamming the store may lead to your removal from the Apple Developer Program.