I think the coin part is self explanatory. As with any currency there is a decimal of that currency too. These decimal or parts that make up the whole to create a whole coin, Often given a title like pound or dollar.
In the case of Bitcoin. The coin is made up from Bits. Bits are the part that make up the whole coin Bitcoin.
In computer language. Things start of with a bit 8 of these bits make up a byte. A Bitcoin would be equal to 1 million bytes. Being a digital asset or currency made up of bits and to be a coin, The combination of them both bring about the term Bitcoin.
Bitcoin is made up of 1 million bits. 1 bit is equal to one Satoshi hence the name Bitcoin.
Hopefully one day it will be worth a million and then each bit or Satoshi will be valued at $1. That would make things a lot easier for everyone to understand.
Satoshi nakamoto was able to accomplish his dream of a digital coin using a binary mathematical solving, consisting of just 0, 1 which is also know as bit. The algorithm was based on computer language with earliest first generation computers which was strictly of computer language consisting of bits. The only name suitable for it was bit- since it's generated in bit into figure and coin- being the token hence *Bitcoin* to illustrate the coin was made from binary manipulation from computer language