That would probably be an interesting etymological (in English) and pronunciation investigation. I see two possibilities, to begin with: the British with their inimical way of mispronouncing foreign words bequeathed us "Moscow". Another is the Russian connection through Alaska, and possible filtering through Inuit, British, and French speakers in Canada and the Yukon, gradually making it to the lower 48 States of the US.
As a note to this: the letter sequence "kva" is not something you encounter in English. People hear what they are used to hearing rather than what is actually said, so there's a good chance people just didn't hear it right, and said it as best they could, using standard English. Another is that nobody heard it pronounced correctly at all, and someone who didn't know Russian made an effort to transliterate the Russian into something approaching English.
Those are all guesses, though. It's an interesting topic.
It's like the whisper game. In a group of people, the first person tells something to another by whispering it, so no one else can hear. The 2nd tells a 3rd, the 3rd a 4th, until you get to the last person. The last person then says or writes what he/she was told, and it is compared to what the first person said. Sometimes, the end product is very different from the beginning statement.
In a similar kind of way, words can change dramatically as they transit from one area to another. The fact is that Russian owned Alaska at one point, and Russians there had contact with the natives and with people from Canada and the lower United States. The changes for "Moscva" becoming "Moscow" in that transit are something one could expect - though I don't know that that is what happened. I think it makes sense this way, even it if's a complete fabrication.
I don't know Dutch or German, so if you're saying that Moscva became Moscow in the hands of those peoples, then that's a very viable 3rd or 4th alternative explanation.
This is all just idle supposition, it's not meant to be definitional at all.
I'm sorry I should have been more specific. The whisper game part makes sense. It's your theory about the word passing through Alaska that doesnn't. It seems much more likely that the name Moskva travelled through mainlaind Europe during the middle ages. Moscow existed since the 12th century. Trade between mainland Europe and Russia or England has always happened. The only logical explanation is that the British got the word from their neighboring countries.
Moscow has been around for a very long time. And the pronunciation of its name has evolved. And the English have known about it for much of the time. Both Russian and English languages have evolved. And the pronunciation changed in different ways in the different languages. In English we used to talk about "the Duchy of Muscovy" - which is much closer than the modern English form.
жить (žitʹ) [ʐɨtʲ] impf (perfective прожи́ть) "to live; to reside": From Proto-Slavic *žiti (compare Belarusian жыць (žycʹ), Ukrainian жи́ти (žýty), Old Church Slavonic жити (žiti)), from Proto-Indo-European *gʷeih₃w- (“to live”). Cognate to Lithuanian gyventi, Sanskrit जीवति (jīvati), Latin vīvō, Old English cwic (“alive”) (English quick), Ancient Greek βίος (bíos), Welsh byw.