What is the best way to add a general title to a Gallery field type?
A quick and dirty way would be to add a text field just above the gallery field, but I am thinking there must be something better, ideally something that would save the gallery title as an attribute of the gallery.
The only way to have a title that can be edited when adding the gallery would be the way you suggest. Either that or building a custom field type based on the gallery field, adding a new field and then storing the information in a different way than ACF does it. https://www.advancedcustomfields.com/resources/creating-a-new-field-type/. ACF stores an array of post IDs for the images in the gallery. There is nowhere to store other information.