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Binance will support token swap. Here is a link to their official post...

https://support.binance.com/hc/en-us/articles/360001649171-Binance-Will-Support-EOS-MainNet-Token-Swap

I need to register Eos token distribution or no need?

There is no need. And BTW now Exodus also allows you to register tokens from within the wallet. You can look into their post. Here is the link
https://support.exodus.io/article/690-how-do-i-register-my-eos-address-inside-exodus