the datas array is added inside the component. Everytime the component re-renders, it is re-initialized to empty array.

Also, on onDayPress prop in the callback function you've added an extra pair of curly brackets

App is getting re-rendered whenever you change states, so const datas=[]; will be initialized as a new array.

One more problem I can foresee is that you call setData(day) and then call datas.push(data) on the same function which won't be applied with your latest data because states' changes are asynchronous

const handlePress=(day)=>{
   setData(day); //`day` is set here but not applied immediately
   setName(`${events[rand]}`)
   datas.push(data); //data is the previous data, not `day`
   console.log(datas);
 }

The full modification can be

const datas=[]; //move your `datas` to the global scope

export default function App() {
 const [data,setData]= useState([]);
 const [activity, setActivity]= useState([])
 const [name, setName] = useState("")

 
 useEffect(()=>{
  // handlePress()
 }, [setData, setName])

 const rand= Math.floor(Math.random(1,5)*4)+1
 const events=["Event A","Event B","Event C","Event D","Event E"]

 const handlePress=(day)=>{
   setData(day); //`data` will be changed later
   setName(`${events[rand]}`)
   datas.push(day); //push `day` directly instead of data
   console.log(datas);
 }
  return (
    <div className="App">
      <Calendar 
        onDayPress={day => {
          {handlePress(day)}
        }}
        
      />
      
    </div>
  );
}

You also should not use useEffect with setters (setData and setName). These setters have nothing to do with side-effects. You should pass state values as dependencies in useEffect.

//whenever `name` or `data` change, `useEffect` will be triggered
useEffect(()=>{
  //TODO: Do your logic here
 }, [data, name])

In react when you update the state , react component is re-rendered . So here when you update state in handlePress() function your component is re-rendered .So your datas array is re-intialized and become empty again . So every time when you push item it will add to 1st position. Hope it will help you.