If Omega-3 is a fatty acid with a single double bond at the third carbon atom from the omega end, then why is it regarded as a polyunsaturate and not a monounsaturate? Are there different Omega-3s with more than one double bond?
The term "omega-3" just denotes that the position of the first double bond in the fatty acid will be at position "3" (counting from the omega end of the chain). It does not mean that there is only one double bond in the fatty acid. The most common omega-3 fatty acids contain between 3 and 6 cis double bonds (therefore they are polyunsaturated).
Here are few examples, again note how they all have a double bond at the third carbon from the omega end of the chain.
α-Linolenic acid (ALA)
Eicosapentaenoic acid (EPA)
Docosahexaenoic acid (DHA)