When I extended the railway station by copying and pasting, the railway station laid by the drone after pasting still had the custom backer name instead of the name I had already modified for the railway station

What version of Factorio and what version of the mod? And by "copying and pasting" you mean via a blueprint, yes? If you can reproduce this, please send the blueprint string you are pasting (paste, then place in your hotbar, right click, and export blueprint string) so I can try to reproduce it.

This mod only changes the "backer name" of an entity, and not the actual name, so the only way I think this could be happening is if your copy source didn't include train station names

The game version is 2.1.11, and the mod version is the latest version. I used "ctrl+c" to copy a section of the railway containing a renamed station, and then used "ctrl+v" to paste it multiple times. The names of the stations I pasted at the beginning were the modified names, while the names of the stations laid by the unmanned aerial vehicle were the names in the backer list, not the preset names in the blueprint
After disabling the module, the pasted station became a normal name. This is a station blueprint I used, and the station name in the blueprint is the "hourglass" icon+"clock" icon

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