The problem with this method is that it's an invasive one. Whatever if the player want to give a name to the save file or not, he'll have the pop-up screen asking for a name.
It's not a breaking issue, but it also mess with Ren'py flow. You can see it by saving twice in a row, the second save slot screenshot will picture the name input screen in place of the game itself.
Therefore, since you're already relying on the screen title, there's a better approach :
Python:
screen file_slots(title):
[...]
# --- The original button
button:
style "page_label"
key_events True
xalign 0.5
action page_name_value.Toggle()
input:
style "page_label_text"
value page_name_value
if title == "Save":
hbox:
text "Name : "
input:
value VariableInputValue('save_name')
The input box will be at the left of the line where the name page is located.
There many advantage, for only one small inconvenient :
First and before all, if the player don't want to give a name to the save, it will be totally transparent for him. No pop-up, and therefore no need to click on a button every time he save the game
Secondly, the value is to enter only once. Generally you name your save file accordingly to the path you follow, and not accordingly to the moment you save ; Ren'py presenting a screenshot and the date and hour when the save have been made helping for that. Therefore your "girlname only - romantic" name will be used a lot of time consecutively. Contrarily to what happen with the pop-up approach, you'll not have to provide the save name every time you save, but just when the name change.
Thirdly, it don't mess with Ren'py flow.
As for the inconvenient, contrarily to what happen with the pop-up approach, the player have to remember that he have to change the name of the save file. But it's just half a problem. If you use a style that make the name itself clearly stand out of the screen, it will act as a reminder :
View attachment 1104078