Does anyone have recommendations for a vendor/solution for cost effective brand awareness research?  Looking to assess for B2B brand in a few large markets in NA & Europe.

I would say Similarweb, which has different market / competitive intelligence tools. Great for digital insights on traffic, marketing channels, ads etc, but not necessarily the best fit if you're looking for offline data. You can also use Kanta, Ipsos or even do some social media listening to have a first sense of a brand

SG Analytics is best for cost effective brand awareness research and its a global company.

That's a pretty vague question - I think most people will agree that you need to determine what type of brand awareness you are looking for. There are design brand awareness, audience awareness, product awareness, competitor awareness, etc.

Ipsos is a very good one, and I think it can be used to majority of market researchs. Another good alternative is Qualtrics or Kantar. And of course, Gartner is very helpful too. 

Ipsos and Gartner are very good, but it depends on your aims and on the specific countries and industries. Can you specify your question further?