Use the custom turtle name consistently across all screens

Capture the turtle's name on the start screen so it is set before the beach,
beaching, and migration screens. Populate the beaching notice and migration
bonus text from turtleName (previously hardcoded 'Shelly'), pre-fill the
rename modal, and send migration-continue straight to the ocean since the
turtle is already named.

app.js

@@ -205,6 +205,11 @@ document.addEventListener('DOMContentLoaded', () => {
   const btnHeal = document.getElementById('btn-action-heal');
   const feedDrawer = document.getElementById('feed-options-drawer');
 
+  // Name inputs / dynamic name labels
+  const inputTurtleNameStart = document.getElementById('input-turtle-name-start');
+  const beachingTurtleName = document.getElementById('beaching-turtle-name');
+  const bonusTurtleName = document.getElementById('bonus-turtle-name');
+
   // HUD Outputs
   const displayTurtleName = document.getElementById('display-turtle-name');
   const displayTurtleSpecies = document.getElementById('display-turtle-species');
@@ -1248,6 +1253,7 @@ document.addEventListener('DOMContentLoaded', () => {
         bonusInfoCard.classList.add('hidden');
       }
 
+      bonusTurtleName.textContent = turtleName;
       modals.migrationSuccess.classList.remove('hidden');
     } else {
       // Fail! Game over
@@ -2185,6 +2191,7 @@ document.addEventListener('DOMContentLoaded', () => {
   // 9. BEACHING / TOURIST SHIELD EVENT
   // ==========================================
   function initBeachingPhase() {
+    beachingTurtleName.textContent = turtleName;
     beachingProgress = 0;
     beachingProgressFill.style.width = '0%';
     beachingProgressText.textContent = '0%';
@@ -2384,6 +2391,7 @@ document.addEventListener('DOMContentLoaded', () => {
 
   // Start Conservation Game
   btnStartGame.addEventListener('click', () => {
+    turtleName = sanitizeName(inputTurtleNameStart.value);
     changeState(STATES.BEACH);
   });
 
@@ -2397,14 +2405,16 @@ document.addEventListener('DOMContentLoaded', () => {
     document.getElementById('beach-tutorial-overlay').classList.add('hidden');
   });
 
-  // Migration Success Continue Action
+  // Migration Success Continue Action — the turtle was already named at the
+  // start, so head straight into the ocean.
   btnMigrationContinue.addEventListener('click', () => {
     modals.migrationSuccess.classList.add('hidden');
-    modals.rename.classList.remove('hidden');
+    changeState(STATES.OCEAN);
   });
 
   // Rename Turtle Action
   btnRenameTurtle.addEventListener('click', () => {
+    document.getElementById('input-turtle-name').value = turtleName;
     modals.rename.classList.remove('hidden');
   });