<form id="teamSelect">
    <input type="radio" name="team" class="team" value="Fenerbahçe" checked>Fenerbahçe<br>
    <input type="radio" name="team" class="team" value="Galatasaray">Galatasaray<br>
    <input type="radio" name="team" class="team" value="Trabzonspor">Trabzonspor<br>
    <textarea id="textHolder" name="editedTeamName"> </textarea><br>
    <button type="submit">Gönder</button>
</form>

$(function(){
  $('#textHolder').val($('input[name=team]:checked').val());
});
$(document).on('change', '.team', function(){
  $('#textHolder').val($(this).val());
});
$(document).on('submit','#teamSelect',function(){
   alert($('#textHolder').val());
});