I don't know if I can help you because I don't know what your stories are about but I can tell you what I do and what I would do:
Well you can make it a name for the school that relates to the story or make it up. For me, I just usually go to a name generator and if I see one that I like, I use it.
As for uniforms... I don't know if I can help you but usually I like to think of ones that uses a dress shirt and blazer/vest (fall or spring), sweater and long sleeve dress shirt (winter). and if they want, a tie or bow, the student's choice with the school crest on the left chest area or on the collar of all the tops. None of those that resemble a sailor suit. The skirts would be up to or below the knees (maybe above the knees to expose those nice legs >.<... if any). But I'd also give them a choice if they want to wear dress pants because why do all Japanese female uniforms must be skirt? If you don't want the pants thing then they can where shorts under their skirts. It just gets on my nerves. For colours, I always imagined red and purple because I like those colours. I wouldn't really be a stickler about accessories so they can wear it if they want just as long as they have uniform on and it's visible (they can dye their hair if they want to!).
These are my ideas but I hope they give you some ideas.