About the name of the covenant, here are some elements that I think could be part of it.
The temple of Mercury and Roswerta (key words: temple, altar, the ceremonial bowl, laurel, Mercury), although it does have some elements of paganism that may not be agreeable to some of the magi (I'm thinking or Aedituus here, which is probably the most pious).
The forest around the covenant (key words: forest, woods, oak) and its haunted nature (key words: ghosts, whispers).
The research focus of the covenant (key words: search, research, quest, path, mystery) or its cooperative/freedom orientation (key words: friend, tolerance, free, unbound)
This can give names such as:
- Quercus Dimitti ("The Freed Oaks")
- Templum Susurris ("The Temple of Whispers")
- Argentum Laurus ("The Silver Laurel")
Those are just example. If we can agree on a concept for the name, than we can explore variants. Unfortunately my Latin is fairly limited, so I have to rely on translation sites.