Has anyone heard of a company from Japan called WiFi Network? Not sure if they are trying to scam me. They are telling me I need to buy some domains which are similar to the trademark I have.

They are not really trying to scam you. But you don't "need" to buy those domains.

Since the expansion of the top level domains (TLDs) on the WEB a few years back Some companies try to protect their trademarks by registering for their name in all TLDs. For example, Ford has Ford.com, but they also have Ford.net, Ford.biz, etc. So if someone goes to those other URLs they will be redirected to the main Ford.com. Not all companies do this or can do this. For example Nissan.com was a domain registered by a NC computer company before Nissan changed from Datsun to Nissan. Nissan Motors sued them and Nissan Computers has been fighting for almost 10 years (Nissan Motor vs. Nissan Computer - Digest.com).
So far successfully.

There are other instances where you may misspell the URL and find yourself on a totally different site. (try goggle.com). So companies do try to protect themselves by buying up similar domains. Since its relative cheap to own a domain, its sort of worth it.