If you want, you can do it by triggering a templater script via hotkey. I recently created a script that does something very similar, here it is modified for your use case:
Script to create note from selection and prepend parent name
<%*
const editor = app.workspace.activeLeaf.view.editor;
let selection = editor.getSelection();
selection = selection.replace(/[#/|^]/g, ""); // remove disallowed characters
const parent = app.workspace.getActiveFile();
const pName = parent.basename;
let childName = selection.split("\n")[0].replace(/[#/|^]/g, "");
childName = pName + " > " + childName + ".md";
let childContent = "parent: [["+pName+"]]\n***\n";
let child = app.vault.getAbstractFileByPath(childName);
if (child) {
console.warn("child note with this name already exists. Using existing file.");
app.vault.modify(child, childContent + await app.vault.read(child))
}
else child = await app.vault.create(childName, childContent);
editor.replaceSelection("[["+childName.slice(0,-3)+"]]");
// Lastly, open the child note in a new pane
const leaf = app.workspace.splitActiveLeaf()
leaf.openFile(child);
app.workspace.setActiveLeaf(leaf);
%>
Then you can trigger it with a hotkey via Hotkeys for templates plugin.
There might be a way to trigger it on note creation like you said, and if there is, I would love to know how to do that as well!