I did a quick test and the result was kinda funny. Correct maybe, as far as Moho was concerned, but funny. Here's what happened...
1. In Photoshop, I made three layers all named Booya but each with a different drawing in the layer. Saved the PSD file.
2. Imported the PSD to Moho and chose the Individually option. As expected, I got three layers named Booya, each with different artwork, just like in Photoshop.
3. Back in Photoshop, I changed the first Booya to Hello, and the third Booya to Oh No, and saved the file.
4. Switched back to Moho and waited for the layers to update automatically.
After a few seconds, the layers updated and I found Moho had added two new layers--at the top of the Layers window was a new Hello layer and at the bottom was a new Oh No layer. The three layers in the middle remained titled Booya but the content of each layer changed to the same Booya artwork I have in Photoshop.
I had only expected the first and second Moho Booya layers change to the new names, but instead Moho saw the layers that were renamed in Photoshop as brand new layers. I can follow how Moho worked out the logic but it wasn't quite what I expected.
Admittedly, this was kind of a weird example and I probably wouldn't do this for real, but maybe I should report this? Or maybe not as I don't know if fixing this might mess up a more normal layer update situation. I'll ask.