Whether it is a district, amphoe, khet, kwaeng, etc. still doesn't change the fact that no person would refer to Sathorn, CNS, or Samyan as "Silom" (let alone "Bangrak" for that matter, unless they want to go to Central )
Personally even I don't refer to some places on Silom Road (think Lebua Sky Bar or Lerdsin Hospital) as Silom.

So the fact that there are people who group anywhere west of Chidlom or Phloenchit as 'Sukhumvit' is kinda crazy to me. Hopefully that doesn't get spread around!