In the following scenario:
We have Parent clip with Child clip embedded. If we navigate to the Clips menu and rename Child Clip to My Child Clip. The embedded clip inside of Parent clip will still be named Child Clip.
When a Clip is included, either in a Track or in another Clip, it is assigned a logical name for use within that location. This name is not necessarily the same as the Repository name, although it starts out that way by default. This name is deliberately not changed when the Repository name is changed, so that existing Clips and Scripts will not break because someone renamed the Clip in the Repository. Also, it is possible that the same clip can be included multiple times, so it must be assigned a unique name so that it can be referenced in paths and Scripts. Finally, the Repository name is only unique within the containing folder, leading to the possibility of two Clips having the same base Repository name being included in the same Clip.
Therefore, the logical name used for the Clips is not physically tied to the Repository name.
You can change the internal name for any nested Clip in the Clip Editor.