How did a tropical storm starting with "D" end up next to a typhoon starting with "T"?
The naming of typhoons, in the north west pacific region, is different to that used by other parts of the world. According to accuweather,


  For typhoons, there is one list with 140 names submitted from nations in the region such as China, Japan, Vietnam and Cambodia. There is no restrictions to how many can be used in a calendar year.
  
  “Unlike hurricanes, lists are not year-specific, so they scroll through the whole list irrespective of calendar
  
  The Philippines are also a part of the list of nations which submit names. However, according to the Philippine Atmospheric, Geophysical and Astronomical Services Administration (PAGASA), they will use local names whenever a cyclone is within the Philippine Area of Responsibility (PAR). 


NOAA has a list of the names for the north west pacific region. At the end of the webpage, in column V of the last table you will see Talim followed by Doksuri, then Khanun. This is why you are seeing Tropical Storm Doksuri just after Tropical Storm Talim.



It appears that Doksuri, which means eagle, Korean, is the replacement name for Nabi. South Korea submitted the name Nabli to the list of typhoon names, but the name Nabi was retired when Typhoon Nabi hit Japan in 2005.

Tropical Storm Doksuri (2017) was initially named Maring by the Philippine authorities.