Why is Russian word “сидеть” (“sidet'” which means “to sit”) so similar with English word “Sydney”?

As others have said: sometimes, coincidence happens.

Sydney was named for Thomas Townshend, 1st Viscount Sydney, and Sidney (surname) derives from Old English sīdan īege, “at the wide island”, i.e. Water-meadow.

Old English sid means “wide, extensive, broad”, and is the ancestor of Modern English side. Wiktionary tells me it comes from Germanic *sīdaz, which comes from Proto-Indo-European *seh₁(i)- ‎(“to send, throw, drop, sow, deposit”).

сидеть, like sit, comes from Proto-Indo-European *sed-, via Proto-Germanic *sitjaną.

So your question, OP, is actually why are *seh₁-d and *sed– so similar. And the answer still is, sometimes, coincidence happens.