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For example, I registered myName.com and I also registered the .net, .info, and .org extensions for myName. I'm wondering if it will hurt my SEO to forward these other TLDs to myName.com?
Won't hurt, but it won't help either.
This is a very common practice.
The only benefit I can think of is by not letting anyone else use those names.
If you will serve the same content on each of the domains it will definitely help your SEO since when redirecting using 301 redirects (as the previous answers comment states), you avoid having duplicate content issues.