Different spellings for Nanjing and Nanking could, but must not, be related to two linguistic facts:

1) In Southern linguistic varieties of Chinese, non-Mandarin speakers tend to pronounce Mandarin words ending in -ing like -in. Clearly an interference from their local linguisti variety of Chinese.

2) To spell Nanjing with "k" where it should be with "j" today is due to the outdated Wade-Giles Romanization system with its traditional "k" spelling for that sound.

3) Spelling Nankin for Nanjing seems to be a mixture of both (1) and (2) and therefore is fully inaccurate.

A good and informative post Turnoi.