As far as I am aware, you can name child themes as anything you want to.
e.g. parent theme: twenty-thirteen, child theme: carrot-cake
The main thing is to refer to the parent in your child theme style.css (https://codex.wordpress.org/Child_Themes) under the 'Template' name.
Many also then require you to import the CSS, as per the example shown in the Codex, but for others just the 'Template' reference is sufficient (e.g. Responsive theme)