Etymology question: Is there a derivative relationship between the name BORG (of Star Trek fame) and the Borgia family dynasty of the 15th and 16th century?

I think it comes from Cyborg

Definition of cyborg:
a person whose body contains mechanical or electrical devices and whose abilities are greater than the abilities of normal humans.

1960s: blend of cyber- and organism.

I think cyborg is correct.

I once wondered about the name Klingon. Here’s a link about that: https://www.google.com/amp/s/heavy.com/entertainment/star-trek/klingon-name-origin/amp/

What @Tropical_Willie said. Star Trek has a history of non-original species names. Remember the Binars? And “Ferenghi” means “foreigner” in Hindi, and Jemadar was a kind of Indian general.

@Tropical_Willie is correct according to Wiki.

A cyborg (/ˈsaɪbɔːrɡ/)—a portmanteau of cybernetic and organism—is a being with both organic and biomechatronic body parts. The term was coined in 1960 by Manfred Clynes and Nathan S. Kline.[1]

It is derived from ‘cyborg’, as previously stated.
Even the motives you ascribe to them do not make any sense.
The Borg are driven to achieve ‘perfection’, by assimilating the desirable biological and technological distinctiveness of the races they conquer.
Honestly, they believe that by assimilating you, they are doing you a favour.