Many ways, but the useState hook is pretty solid especially if you want to take advantage of React's speed.

import Data from "./names.json";

export default function App() {
  const [ txt, setTxt ] = useState(""); // sets it to an empty string to begin with
  
  useEffect(() => {
    console.log(txt); // every time the 'txt' variable changes, log it
  }, [ txt]); // << React calls this a dependency and will only run this function when this value changes.

  console.log(txt); // also accessible here

  return (
    <div className="App">
      {Data.map((post) => {
        setTxt(post.Name); // This updates the 'txt' variable from earlier ^^
        return <h1>{post.Name}</h1>;
      })}
    </div>
  );
}

If all that is too long-winded, just keep your txt variable outside of the function component, and React won't reset it every loop. You'll still be able to access its value anywhere in the file. Example:

import Data from "./names.json";
let txt = "";

export default function App() {
  return (
    <div className="App">
      {Data.map((post) => {
        txt = post.Name;
        return <h1>{post.Name}</h1>;
      })}
    </div>
  );
}

afaik you can't because text is scoped to the map function and you can't access it outside of it. You can try putting it in a state or make a function and make it an argument of that function from inside the map function.

import Data from "./names.json";
import {useState} from 'react'
export default function App() {
  //want to access txt in here <==============
  // console.log(txt) and stuff after accessing it here
  const [text,setText] = useState()
  function getText(text) {
    console.log(text) // this function gets called in every instance of the map loop
    //you can run your logic here to find specific information and then set it to the state like in this example
    if (text === "myText") {
        setText(text)
    }
  }
  
  return (
    <div className="App">
      {Data.map((post) => {
        var txt = post.Name;
        getText(txt) // will run and recieve the var txt every instance
        return <h1>{post.Name}</h1>;
      })}
    </div>
  );
}