using "the" with the name assigned to a part of a device

Impossible to answer without example.

The following paragraph is an example for describing my device which is comprised of two part and I named them i-part and c-part:
"My new device has two part, namely, i-part and c-part. i-part receives the data from another device and deliver it to c-part. c-part calculates the necessary variables required to encrypt the information"
my question is: where should I use "the" before i-part and c-part?
if I name the part I-part and C-part, what should I do?

If you give a thing a "proper name," then I don't think you would add "the" before it.

You wouldn't say "The Barrack Obama said.....," for example. Nor would you say "The Florida has a lot of sunshine."

But your chosen terminology here is ambiguous. By including the word "part" in the "name" (or some similar word such as "function") it doesn't sound like a proper name. It sounds like a common noun.

My new device has two parts: the (or an) i-part and and the (or a) c-part. The i-part receives the data from another device and delivers it to the c-part, which calculates the necessary variables required to encrypt the information.