You need to mark the parameter as excluded. See https://allurereport.org/docs/how-it-works-test-result-file/#parameters-array for details:

Then("do something", async () => {
  await allure.parameter('randomNumber', Math.random(), { excluded: true }); 
});

I tried your proposal, but it seems you got me wrong.

My expectation is, that when running the same test several times and just a parameter changing, allure creates different entries.

But currently I only see one of the entries, even with your suggestion.

When adding e.g. the version hash to the historyId, I get the above result, as expected.

I tried to reproduce the problem. However, I had no luck:

As you suggested, I added the dynamic parameter:

import { Given } from "@cucumber/cucumber";
import { parameter } from "allure-js-commons";

Given("sample step", async function () {
  await parameter('randomNumber',String(Math.random()));
});

when I run tests two times:

$ npm test
$ npm test

then, the report shows two different results as expected

if I exclude the dynamic parameter

import { Given } from "@cucumber/cucumber";
import { parameter } from "allure-js-commons";

Given("sample step", async function () {
  await parameter('randomNumber',String(Math.random()), { excluded: true });
});

then only the last result is shown:

It looks to me like everything works as expected. The example I used: https://github.com/allure-examples/cucumberjs-npm-cjs-ts.

When taking a look at your response, I had an idea:
We are adding the parameter in the Before hook.
I tried it locally: If I add a random parameter in the Given step, everything works properly. If I add the random parameter in the Before hook, I get the above described behavior.

Sorry for the wrong example above - I thought this is a general problem.

Can you reproduce it, when adding the parameter in the hook?

Yes, according to the code, we set the historyId before we process parameters from hooks.