Because spelling was not standardized in the 14th Century, each scribe wrote words the way that they sounded to him.
In the documents written in Katharine’s own time, (many of which John of Gaunt dictated to his scribes) her name was spelled many different ways, including: Kateryn Swynford and Kateryne Swynford. Swynford is also sometimes spelled Swinford as in Katherine Swinford or Katharine Swinford.
The most common modern spelling of her name is Katherine Swynford and this spelling was probably popularized by Anya Seton when she wrote her famous book ‘Katherine’ in 1954.
In modern spelling there are also various spellings of: Catherine Swynford, Catherine Swinford, Catharine Swynford and Catharine Swinford.
I have chosen the more unique spelling of Katharine – spelling her first name with an ‘a’ in the second syllable.