Renaming target node of MultiplayerSynchronizer results in broken synchronization with wrong node being shown in replication tab

[benjo121ben]

Tested versions

• Detected in 4.4.beta3
• can be replicated in 4.3.stable
• likely to be the same issue as #92520

System information

Windows 10 - Godot 4.4.beta3

Issue description

If a node, which is targeted by a multiplayer synchronizer gets renamed, several things happen

• its name is not changed for the synchronization logic, as now the synchronizer will throw an error looking for the old node name
• its name is changed in the replication tab, which now shows the name of the scenes root node instead

The issue is mostly problematic, not because of the errors being thrown, but because it is really hard to spot the wrong entries inside the replication tab in larger projects

Steps to reproduce

1. create a scene
2. add a multiplayer synchronizer and another node of any type, for this example i will name it "TestNode"

3. select a property of "TestNode" for synchronization, any property can be selected

4. rename "TestNode" to any other name

5. check replication tab of multiplayer synchronizer, which now shows the root node being synchronized instead

Minimal reproduction project (MRP)

N/A