The Household Keepers is a long-lived group and its founding dates before RBR. During RBR it continued to exist under Citizen Arbory, a collaborator with Doctor Robotnik who deposed the duchal family, and was effectively Arbory's secret police - although this group was really only the 'Household Keepers' in name as most of the original duchal loyalists either fled during the Zone's takeover or were destroyed in the later Fratricide, although some survivors did stay on for RBR. With the restoration of the old regime following RBR's end, the Keepers have also reassumed their former, non-oppressive, role.
Their name derives from their seeing themselves as the keen-eyed guardians of the Duke and his possessions; 'protection of the people' is not a stated priority, it only comes from a noble's obligations of service to help and sustain his subjects, which the Keepers represent as agents of the Duke. It still results in the protection of peace and tranquility for the people - well, as much as there can be in a zone constantly wracked with earthquakes and volcanic eruptions - but there is some distinction in the perspective.
All Keepers are strictly and exhaustively vetted for their ardent loyalty to the duchy and commitment to its preservation. This, combined with the Hill Top Zone's natural culture of social heirarchy and strong familial and zonal bonds, means that the Household Keepers have perhaps the highest level of integrity and security amongst espionage organisations and rarely suffer from leaks or traitors. It does put some limitations on their field effectiveness, though - in the spying game you frequently have to deal with untrustworthy types and cut deals with some villains to pursue others, which Keepers from their nature are sometimes reluctant to do.
Although each Keeper has weapons training and the Household Keepers also maintain a small special forces unit, the organisation itself is not a military force. The Hill Top Zone maintains its own armed forces, and provides shelter to the Bounder Brigade, for the purposes of fighting wars.
While it's not used by field agents for obvious reasons of maintaining cover, office-working Keepers, or Keepers specifically required to be seen in public, wear a characteristic uniform of a black shirt with a red tie (which can be patterned, according to individual taste) and light brown trousers. It's not known whether you are actually contractually required to smoke in order to pass muster for the Keepers, but it's been statistically proven that living within a quarter-mile of the Household Keepers' headquarters building will treble your chance of contracting lung cancer...