So there are two parts to your question. Other answers have given a plethora of sources and interesting background detail, but I think I'll just directly answer the two facets of the question.
- How did Yoda know this was a war, not a skirmish?
- Why was it called
Clone War instead of something else?
As for why it was known to Yoda to be the beginning of a war, others have pointed out with great detail that tensions had been brewing for decades, and faults had already emerged. Kenobi's transmission back to Coruscant is particularly enlightening for the Jedi Council, as it confirms the lines have been drawn for a full-scale conflict, rather than just tense relations leading to outbreaks of violence in a scattered manner.
Regarding the use of
Clone as an adjective for the war, there are several possibilities for this. Importantly, Kenobi seems very uncomfortable with the concept of a clone army throughout the movie. To me, it seems clear that there is a stigma to clones in the Republic, just as we have qualms about clones today. Some of this could be attributed to the Jedi's view that the Republic should not militarize itself, but I feel some is due to a prejudice specifically regarding clones. Regardless of clone's stigma (or lack thereof) it is clear that a clone army was not the norm historically, or at that time. That makes clones perhaps the most notable feature of this war, rather than the two sides.