Should you mention your sources of inspiration somewhere? Let's say you borrow a lot from Greek mythology, Shakespeare, and take some world-building ideas from some famous author. Should you mention them in your book somewhere. How is this usually done? I am assuming some famous authors are open and fully transparent about this.
David Drake often includes an "Author's Notes" section in his novels.
These are placed before the text of the novel. You can skip them, and I suspect many people do.
If you read them, though, you will find some insights into how current events and ancient history combined to produce the story. There are often times anecdotes about how characters, things, or places got their names or descriptions.
I enjoy the "Author's Notes" as much as I enjoy the stories.
It is a rare story that doesn't share some plot elements with older works. Sometimes it is purely coincidental, sometimes it is deliberate.
Any "road story" is going to have elements of Homer's Odyssey in it. Even if you've never read it, just writing an interesting "road story" will involve things that happened to Odysseus. There will be things that hinder the trip, and things that tempt your hero to give up the quest, etc.
In the same way, pretty much any new story will bear some similarity to earlier stories.
It is also fairly common to write a story that uses characters from mythology - complete with their names and attributes.
Some of the most realistic stories come from authors who know history and mythology, and who can meld them with their own ideas to carry their own messages.
Authors like Drake give you a window into the thoughts that go into making something fresh and modern out of ancient history.
As you have added the tag "copyright" to your question, let me first clarify that inspirations are irrelevant to copyright, there is no legal obligation in any form in this case.
The usual way is to have an acknowledgment section at the end of your book where you can thank everyone involved in the project and where you could include a list of people who have inspired you.
Easter Egg hunt:
I will shamelessly admit I take inspiration from all sorts of global mythologies. But I'm not inserting a shoutout to Homer in my books. Instead, I place references, names and allusions to the things I take inspirations from into my book. For those who are fans of mythology (or who like to Google everything) My work is filled with Easter eggs.
So I wrote a novel inspired in part by several Greek gods and characters who interacted with them. After my initial draft, I realized my book shared significant similarities to the Oresteia, a cycle of Greek plays that function a bit like the backstory to the Trojan war. Rather than trying to make the book less like the Oresteia, I decided to enhance this. As I edited, I added small additional references, or accentuated the things that were already similar. So now Artemis, Nemesis and the Furies are central names in the work, and if you read it, you can clearly see Clytemnestra reflected in the mothers of the story. While I didn't change the parts of the story that DIDN'T follow the Oresteia, even here there are subtle tie-ins to Helen of Troy (Clytemnestra's twin sister).
Anyone who finds a name in my book can Google it, and will probably find some kind of tie-in to where the character or story line came from. So a clever reader would know that if there are three brothers of the Heydrich family, and the two surviving brothers are named Eugen and Tristan, they could tell me the name of the remaining brother even though it never appears in the story.
So reward your diligent and curious readers with pretiola (Google it, it's the origin of the word pretzel). Someone who doesn't care won't pay that much attention, and those who do will feel like they're in on a secret.