Nowadays in Russia the Russians are called 'Russians' by non-Russian people. And the Russians themselves call themselves 'Russians'. Never 'Big Russian', no 'Great Russians'.
If in everyday ordinary conversation some Russian called himself 'Great(big) Russian' the other Russians would laugh their asses off

.
Because it sounds very old-fashioned and actually funny.
I was about twelve years old when I first got to know (learned) during a History lesson at school, that the Russians were called Velikorossy (великороссы) in the 19-th century and early in the 20-th century.
I was quite surprised.
Historically there was 'Little (small) Russia' - Ukraine. And the Ukrainians were called 'Small(little) Russians' - malorossy (малороссы). It is definitely about the size, not about 'inferiority' or 'insignificance' or 'defectiveness' or anything like that.
As opposed to them the inhabitants of 'Proper Russia' which was definitely bigger in size were called 'velikorossy' (великороссы). But it is about the size of the country, it has nothing to do with 'grandeur' or 'majesty' or 'mightiness' or anything like that.
So if after reading the above you still want to translate ‘Velikorossy’ into English the better choice is 'Big Russians'. In my opinion.