If there was anybody that would establish a new department in a magical government, what would you call it?
I have several names for such and a summary of what they are.
Department of Magical Defense
The Department of Magical Defense (or DMD) is a department of the Magical Congress of the United States of America that controls and oversees the authority of magical defenses against magical threats and/or terrorism against wizarding America, whether they are domestic or international. The department's head is the Secretary of Magical Defense, who answers to the President of MACUSA and has authority over the Department of Magical Law Enforcement in extreme cases of emergency. This department is the wizarding equivalent of the United States Department of Defense.
Department of Mundane Affairs and Relations
The Department of Mundane Affairs and Relations (or DMAR) is a department of the Magical Congress of the United States of America that is dedicated to the collaboration of peace and diplomacy between wizardkind and mundanes and was first established after the repealing of Rappaport's Law in 1965. The department's head is the Secretary of Mundane Affairs, which serves as an ambassadorial-type where not only wizards and witches work with mundanes that are "in-the-know" of the existence of the wizarding world, but also squibs who help maintain secrecy of the existence of the wizarding world from other mundanes that do not know of wizardkind's existence.
Department for the Welfare and Protection of Magical Children
The Department for the Welfare and Protection of Magical Children (DWPMC) is a department of the Magical Congress of the United States of America that is dedicated to the protection of newblood and half-blood wizards and witches and was first established and created in response to the Obscurial attack in New York City in 1926 and after the repealing of Rappaport's Law in 1965. When a newblood wizard's or witch's magic manifests, a representative of Ilvermorny, MACUSA, or another wizarding school is sent to the mundane homes to inform the families of the existence of magic, the wizarding world, MACUSA, and every known wizarding school in America where the families are told about the National Statute of Secrecy all the while giving newbloods their acceptance letters to whichever school along with adding that they are now under the jurisdiction of wizarding law with MACUSA, too. The mundane families are allowed to inform immediate family members (e.g., grandparents, siblings, aunts, uncles, and cousins) about the wizarding world as well if they have any, but they must be sworn to secrecy about it to be kept only between family, therefore making them "in-the-know" of the existence of magic. However, if the families reacts negatively (especially with any permutations of child abuse, neglect, and endangerment) towards their children in response to being wizards and/or witches, irrespective of relations, whether out of religious discrimination, fear, jealousy, or however else, the newblood wizards and witches are immediately placed in a magical welfare and foster care system (i.e., orphanages) with social workers being assigned to the newbloods (including half-bloods and part-creatures) and the families will be obliviated of the existence of the wizarding world and their children that are magical, this also includes other relatives that prove to be unfit for guardianship (mostly for half-bloods). But, if the families react with positivity and openmindedness, the department allows some of the mundane families to help serve as foster families to other newblood and/or half-blood wizards and witches if they wish. This department is the wizarding equivalent of child protective services.
Department of Magical Research and Development
The Department of Magical Research and Development (or DMRD) is a department of the Magical Congress of the United States of America that is dedicated to the research of unknown, forgotten, obscured, and new magic, including that of technomancy and crystallomancy, a cure and magical therapeutics for lycanthropy, magical allergens for animal, food, and plant allergies, cures for photosensitivities (including xeroderma pigmentosum), and replicating fossil fuels by trying to preserve said resources and possibly stimulate them, too. Most of those in technomancy and crystallomancy have to need approval for possible new classes to be taken at every American wizarding school. The department also has a high-security magical vault similar to the Garm Vault and Anubis Vault incorporated with very powerful Anti-Unlocking Charms and Anti-Lockpicking Charms that keeps every bit of known magical research inside, whether written or created and with a powerfully modified and inexhaustible Flagrante Curse and Anti-Theft Charm that works only on dark forces, corrupt/dishonest politicians, thieves, and other despots, irrespective of their magical blood statuses and nationalities, even if there are Imperiused people so to keep every item from being stolen, and can only be accessed by the President of MACUSA and the Head of the Department. This department is the American equivalent of a Department of Mysteries.
Department for the Magical Restoration of National Treasures
The Department for the Magical Restoration of National Treasures (or DMRNT) is a department of the Magical Congress of the United States of America that magically restores and repairs magical accidents of mundane historic treasures, properties, landmarks, monuments, and public art all across the United States when said structures, areas, facilities, and sculptures are damaged and/or vandalized by unusual means. The treasures are all magically repaired and cleaned to the point as if nothing ever happened along with placing very powerful protective enchantments on them, too. This department is the American equivalent of a Department of Magical Accidents and Catastrophes.
Magical Agency of Intelligence
The Magical Agency of Intelligence (or MAI) is a magical foreign intelligence service of the Magical Congress of the United States of America that is tasked with gathering, processing, and analyzing national security information from all over the wizarding world, that of which includes dark forces, corrupt/dishonest politicians, and other despots, both domestic and international. The agency's head is the Director of Magical Intelligence, who like the Secretary of Magical Defense also answers and reports to the President of MACUSA. This agency is the wizarding equivalent of the Central Intelligence Agency.
Magical Security Agency
The Magical Security Agency (MSA) is a magical intelligence agency of MACUSA's Department of Magical Defense under the authority of the Secretary of Magical Defense. The MSA is responsible for global monitoring, collection, and processing of information and data for foreign and domestic intelligence and counterintelligence purposes of all magical knowledge, both common, forbidden, lost, and forgotten. The agency's head is the Director of Magical Security who answers to the Secretary of Magical Defense along with the President of MACUSA. This agency is the wizarding equivalent of the National Security Agency.