Here is a list of all the canon characters in the Next Generation Era. If I'm missing someone feel free to hit me up with a PM and I'll add them. For the adults I only really put the major characters, if you want one of the minor ones feel free to put in an application for them and I'll add them here.
Adults
Arthur Weasley - Unclaimed
Molly Weasley - Unclaimed
William 'Bill' Weasley - Unclaimed
Fleur Weasley nee Delacour - Unclaimed
Charlie Weasley - Unclaimed
Percival Weasley - Unclaimed
Audrey Weasley - Unclaimed
Ronald 'Ron' Weasley - Unclaimed
Hermione Weasley nee Granger - Unclaimed
Harry Potter - Unclaimed
Ginny Potter nee Weasley - Unclaimed
Geroge Weasley - Unclaimed
Angelina Weasley nee Johnson - Unclaimed
Kingsley Shacklebolt - Unclaimed
Narcissa Malfoy - Unclaimed
Lucius Malfoy - Unclaimed
Draco Malfoy - Unclaimed
Astoria Malfoy nee Greengrass - Unclaimed
Andromeda Tonks - Unclaimed
Ted Tonks - Unclaimed
Viktor Krum - Unclaimed
Xenophilous Lovegood - Unclaimed
Lee Jordan - Unclaimed
Alicia Spinnet - Unclaimed
Katie Bell - Unclaimed
Dean Thomas - Unclaimed
Hannah Longbottom nee Abbott - Unclaimed
Susan Bones - Unclaimed
Terry Boot - Unclaimed
Padma Patil - Unclaimed
Luna Scamander nee Lovegood - Unclaimed
Rolf Scamander - Unclaimed
Millicent Bulstrode - Unclaimed
Tracey Davis - Unclaimed
Daphne Greengrass - Unclaimed
Theodore Nott - Unclaimed
Pansy Parkinson - Unclaimed
Blaise Zabini - Unclaimed
Professors
Headmistress, Minerva McGonagall - Unclaimed
Charms Professor, Filius Flitwick - Unclaimed
History of Magic Professor, Cuthbert Binns - Unclaimed
Care of Magical Creatures Professor, Hagrid - Unclaimed
Herbology Professor, Neville Longbottom - Unclaimed
Arithmancy Professor, Septima Vector - Unclaimed
Astronomy Professor, Aurora Sinistra - Unclaimed
Divination Professor, Sybill Trelawney/Firenze - Unclaimed
Flying Professor and Quidditch Ref, Rolanda Hooch - Unclaimed
Ancient Runes Professor, Bathsheda Babbling - Unclaimed
Medi-Witch, Poppy Pomfrey - Unclaimed
Students
All of these are only the ones that JK Rowling has confirmed; if there is any more that I don't know of feel free to hit me up with a PM and I'll add them.
Graduated StudentsTheodre 'Teddy' Lupin - Unclaimed
Victorie Weasley - Unclaimed
Students (going from the oldest to the youngest; since some of the children houses are unknown I won't go by house)7th Year, Dominique Weasley - Unclaimed
5th Year, Louis Weasley - Unclaimed
5th Year, Molly Weasley - Unclaimed
4th Year, Fred Weasley II - Unclaimed
4th Year Gryffindor, James Sirius Potter - Unclaimed
3rd Year, Rose Weasley - Unclaimed
3rd Year Slytherin, Albus Severus Potter - Unclaimed
3rd Year Slytherin, Scorpius Hyperion Malfoy - Unclaimed
1st Year, Roxanne Weasley - Unclaimed
1st Year, Lucy Weasley - Unclaimed
1st Year Gryffindor, Lily Luna Potter - Unclaimed
1st Year (Possible) Lorcan Scamander - Unclaimed
1st Year (Possible) Lysander Scamander - Unclaimed