Reproduction steps:
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1) Open user's project
2) Make sure that 'Assets -> Data' folder is empty
3) From the menu bar select 'Run -> Mesh Generation B 1'
--- Five mesh assets will be created each with five mesh children
--- All of the children should be named in this manner: 'X_Submesh_Y'
--- One of them however is named 'MeshY', same as the parent mesh
4) Save project
--- Another child mesh should rename itself from 'X_Submesh_Y' to 'MeshY'
--- If you repeat step 4) all of the children meshes will be renamed

Regression introduced in 5.3.3p1