I think you can do that with the default app but I don’t use Ubuntu/Gnome and may be wrong. I hope this link may give you a starting point: https://www.tecmint.com/take-or-capture-desktop-screenshots-in-ubuntu-linux/

Try flameshot.

I like using the tool called “import”. It’s a command line program that takes a filename for it to write to. It gives you the option to write whatever save name logic you want around it.

The utility is open source, right? You could change the default save name in the source code. That actually would not be a difficult change to make, and if you are confident enough you could even submit a patch to make it configurable.