I made a few edits to the registry, rewording and adding a little bit to hopefully clear up some of the confusion:
One may also report to Hanei a wizard they know exists in the city who is unregistered, and runs the risk of overgiving and thus endangering other members of the city. The process is quick and simple, involving the signing of one form which states that you are indeed a practitioner of magic and gives the permission for the Shinya to detain you if necessary. The three main houses endorse the Wizard Registry, and when one registers he is given access to resources not made available to non registered wizards. This information allows for the registered Wizard to petition their particular supporting house for things such as loans for businesses and access to specific parts of the Library, and perhaps even request jobs related to their magical abilities. Once the official forms are signed the Wizard is given a patch they must wear at all times with the symbol of the House they fall under.
Wizard's are registered under the house that supports what they consider their main magic, but of course given the fluid nature of magics and their practitioners once per season a mage or wizard can re register under a different house that more closely supports their needs. The Dawn House supports Reimancers, Shielders, Flux users and Magecrafters. Dusk house supports Aurist, Spiritist, and Summoners. Twilight House supports Morphers, Alchemist and Animators. Leechers and Hypnotist are not supported by any of the main houses as these magics are seen as disruptive to the community, but simply having these magics registered will not affect a person's job availability. Glyphers may be supported by any of the houses though if Glyphing is chosen as one's main magic it is unlikely any work will be made available. Malediction and Voiding are not supported directly by any of the house, and it is rare that any work is available for those who practice these disciplines. Projection is under the direct supervision of the Shinya. Having any of these magics is acceptable within the city, however, the practice of some such as leeching and hypnotism in a way that is not permitted will cause quick and drastic consequences. It should be noted that while all Wizards must register and wear the patch of their house, they are under no obligation to tell others what their particular magics are. Simply wearing the patch is a sign of prestige and will give access to the Wizards only locations and make other possibilities open within the three main houses.
Youchi Dawn of the Cosmos Center always directs those new wizards in Lhavit to the registry, as well as many of the denizens. A new wizard will always be made aware of it, as many of the citizens are wary of being in the way of overgiving. It is a social responsibility to make sure all magic is accounted for. It is to be noted, however, that just because one registers at the Wizard Registry they are under no obligation to take a job using one of their magics, or accepting any jobs that are offered to them. They are free to choose whether or not they wish to use any of the resources made available to them and are also allowed to practice their own magic within the safety of their own home or the Wizards only locations.
OK so by main magics I typically mean the one that the character's themselves consider their favorite, or most proficient and does not necessarily have to reflect their actual skill level. It can even be the one they are most interested with at the time. I have readjusted the location so that we can account for the nature of mages and their shifting attention spans, so once a season you may re register under a different house

I changed a little of the wording here as well. I did not mean 'under the authority' as in these are the ones that are going to policy you 24/7. Its more like if you are interested in these types of magics THIS house will be able to support you and provide you resources if you need them. I wanted a real reason and way ICly for players to gain access to the houses without being a part of the house, and without just making the houses fully open to everyone. Since I am taking away the option to tutor under the houses in magic I decided to open them up more as a source for information and resources for current mages. So if you are a reimancer and you want to start a business with reimancy you simply need to petition the Dawn House that supports all reimancy activities in Lhavit. Since you are already registered under them it makes the process all the easier and you do not have to go through the beginning paper work process where they figure out who you are and if you are trust worthy to provide extra information and loans to. You could be a reimancer with skill in Animation and you could definitely still talk to the Twilight house for loans for a business, however, the process will be longer and a little more involved than if you first talked with the house who you are registered to because they already have your information.
I have only patches listed for now, but I fully intended to add a few other options such as medallions, gloves and possibly simple shirts and dresses with the symbol of the house on it. I am also playing with the idea that if you simply have the symbol of a house on your clothing somewhere you are automatically considered a mage, and it would be a serious offense to try and impersonate a mage to gain access to their resources

. Still I believe that would be a fun option to provide. The Symbols of the houses grant the mage access to resources non mages do not have, makes it a little easier for them to gain loans and other such things from the house that they fall under, and of course gives them access to the Wizards Only location. Yes as a mage they are required to register as it is law, and so they should wear something that signifies they are a mage, BUT that does not mean that they have to work using their magic. A Master Morpher could simply run a flower stand and it would be perfectly alright. it is important to remember that all of these things are put here to give some structure and open more opportunities for players, but it is up to the players to utilize them.
Finally, Lhavit as a whole is accepting to the IDEA of every magic. Just because you do practice Hypnotism that will not hold you back in anyway, you know as long as you don't get caught using it on people lol. Now as I say in the write up however the patches/symbols only mark you as a Wizard or mage, but you are under no obligations at all to tell anyone what magics you use. You have to register all of them with the registry yes, but that is simply for the 3 houses benefits as well as the Shinya's in case action is ever needed to be taken to either stop you, or help you should you go into overgiving. Everyone else though? They just see that you are a mage and in Lhavit all mages are equal. Does that make sense?
If you have more questions please feel free to ask. I am still debating over a single location or a small district of sorts with 2 or 3 locations made available. If it is the later I will need to investigate further into a proper place to put it with Lhavit's layout. Let me know your thoughts

Mirage