Russkoje tsarstvo later changed to Rossiyskoye tsarstvo.
Why is the English name of the country "Russia" not spelled "Rossia"?
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And in general, the Russians pronounce their country as RAssia.
This is true, but (unlike English) they put the stress on the second syllable, so the first vowel becomes a schwa-like sound. 'rasSIa' would be a better representation for those of us (myself included) who don't regular use IPA.
English is a rather unique language in many senses, one of them being that all vowels can reduce to a schwa. In this case, the u. Also, what @Spencer says: "Why do you expect anything about English spelling to make sense?"
What you have here is one instance of a larger question: why do English speakers (and I presume speakers of other languages*) often use different names for foreign countries than the inhabitants of those countries do? For instance: Spain/España, Germany/Deutschland, Finland/Suomi, Japan/Nihon…
"Russia" is in fact exactly how (most) English speakers pronounce the name of the country.