They should have an original name, and any time they are renamed reuse that original name for new.
For example, a 3-deep container is currently named:
SuperComplexNetwork_complexNet1_firstHalf_ComplexNetwork_firstHalf_wifi_1 ^ Layer 1 ^2 ^3 ^overriden template ^overriden ^actual container name (wifi_1)
They should have an original name, and any time they are renamed reuse that original name for new.
For example, a 3-deep container is currently named:
SuperComplexNetwork_complexNet1_firstHalf_ComplexNetwork_firstHalf_wifi_1 ^ Layer 1 ^2 ^3 ^overriden template ^overriden ^actual container name (wifi_1)