I am new to EOSIO, I leart that NETWORK, CPU and RAM can be purchased by EOS coin. The question is if I build a private blockchain and do I still need EOS coin to purchase these resources?
No. A private eosio blockchain will have it's own token to use for resource allocation.
You can check more information on the developers documentation here: https://developers.eos.io/
Check this https://developers.eos.io/welcome/latest/tutorials/bios-boot-sequence tutorial it may help you to understand it better.