I asked Brendan Eich (the creator of JavaScript) if he picked those names on Twitter and he responded:
Old Unix names, hard to find man pages rn but see https://www.unix.com/man-page/minix/1/btoa/ …. The names carried over from Unix into the Netscape codebase. I reflected them into JS in a big hurry in 1995 (after the ten days in May but soon).
In case the Minix link breaks, here's the man page content:
BTOA(1) BTOA(1)
NAME
btoa - binary to ascii conversion
SYNOPSIS
btoa [-adhor] [infile] [outfile]
OPTIONS
-a Decode, rather than encode, the file
-d Extracts repair file from diagnosis file
-h Help menu is displayed giving the options
-o The obsolete algorithm is used for backward compatibility
-r Repair a damaged file
EXAMPLES
btoa <a.out >a.btoa # Convert a.out to ASCII
btoa -a <a.btoa >a.out
# Reverse the above
DESCRIPTION
Btoa is a filter that converts a binary file to ascii for transmission over a telephone
line. If two file names are provided, the first in used for input and the second for out-
put. If only one is provided, it is used as the input file. The program is a function-
ally similar alternative to uue/uud, but the encoding is completely different. Since both
of these are widely used, both have been provided with MINIX. The file is expanded about
25 percent in the process.
SEE ALSO
uue(1), uud(1).
The atob() and btoa() methods allow authors to transform content to and from the base64 encoding.
In these APIs, for mnemonic purposes, the "b" can be considered to stand for "binary", and the "a" for "ASCII". In practice, though, for primarily historical reasons, both the input and output of these functions are Unicode strings.
From : http://www.w3.org/TR/html/webappapis.html#atob