The Name Derives from the Program/Process Created to Read it
The most interesting answer I found on the subject suggest that the name of the language came as a result of the name of the program written to translate it to machine code.
Quora.com user David Gish, who stated:
"In the very early days of computing, programmers wrote code in binary
machine instructions and entered it into the computer through a bank
of toggle switches.
This was tedious, to say the least.
They could ease the pain somewhat by coding in octal (base 8) —
translating between binary and octal is quite trivial — but the code
still had to be entered in binary through the switch bank.
Editing the code was a nightmare.
Inserting an instruction meant changing the memory addresses of
everything that followed it.
It was much easier to write and read the code in a symbolic form while
working on it. Instead of laboring with memory addresses, symbols and
labels were used and the step of translating it to binary machine code
was deferred until the program was finished.
At this point the programmer would convert each symbolic instruction
to its binary equivalent, which became known as “assembling” the
program.
It wasn’t long before someone wrote a program to do the job, and
naturally named it the “assembler.”
In a backward way, the symbolic instructions became known as . . . “assembly” code."
Maybe it should be written as "assemblee"
So, being the Etymologist that I am, it got me thinking about the idea that maybe the original term would have been more appropriately written as "assemblee" and defined as "that which is assembled".
This falls in line with terms very often used in the financial world:
"Payor" and "Payee"
"Mortgagor" and "Mortgagee"
"Assembler" and "Assemblee"