How to add custom name to allready inserted components?

I can do that by adding data-gjs-custom-name="myname"

Use name instead of custom-name (this one is used for Layers when you edit them), so data-gjs-name="myname"

How is it possible to put a name on all h1, for example?

You can create a custom component to extend the definition for H1 elements, so this will be applied to all H1 (even added lately) or you can do it interactively only on the components in the canvas in this way

editor.getWrapper().find('h1').forEach(
	component => component.set('name', 'Name H1')
)