For Edward, the Latin equivalent apparently, is Eduardus, so Eduardia would follow from Georgia, etc. James would get J/Iacobia or J/Iacomia, Charles > Carolia, William > Gulielmia or Vilhelmia, etc.
As others have said, you could use their regnal number as a base, e.g. "Octavia", or a contemporary (positive) epithet, e.g. "Virginia".
There's always colony names based on calqued names as well, i.e. literal translations of the name. "Edward", for example, means something along the lines of "Guardian of Wealth" or "Prosperous Protector". From there you could take, "protector" as as have Patronia.