Gladys comes from the old Welsh name Gwladus, derived from gwlad ("country"). The Welsh name can be translated into English as the given name Claudia (Behind the Name).
Boothby is a English surname of Norse-Viking origin, after villages in Lincolnshire. It means "the farm with the stables" and is pre-8th century (Internet Surname Database).
Lexicon list of Broom Manufacturers
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WizardingWorld.com (Pottermore) features:
Harry Potter Wiki: Brooms