Is canis majoris canis major

Answer 1

Not precisely.

Canis major translated from Latin to English is "the great dog".

Canis majoris translated from Latin to English is "of the great dog", or "the great dog's".

("Great" in both of those is meant in the sense of "big, large", not in the sense of "wow, what a fantastic dog.")

Answer 2

Canis Majoris is not the name of a specific celestial body or constellation. Canis Major, however, is a constellation in the southern sky containing the bright star Sirius.