i've been working since the mid-1990s on the stix project, whose goal was to
add math and technical symbols to unicode. (several thousand added, largely
effective with unicode 4.0, and still growing very slowly.)
a chronology of this project, with data tables showing unicodes and (tex) command names, can be found at http://www.ams.org/STIX/ ; it is not up to
date, problems having arisen, mainly with respect to the pua (unicode
private use area), and agreed upon but not implemented changes to names
associated with some of the math alphanumerics. however, i believe the
names in the table were used in implementation of the xits font, and they
will certainly be used for the stix fonts.
obviously, as new symbols keep being devised, not every symbol has a unicode.
however, the unicode technical committee is amenable to additions, provided
a request can be documented by evidence in an article or book from a
"recognized" publisher; such evidence would best include an example in
context, preferably with the context indicating meaning and intended usage.
as it pertains to this question, the table described here is in unicode
order. there is a lot of extra "baggage" in the table, but it should be
possible to recognize a unicode and the associated command name without
difficulty. (if any errors are spotted, please send word to the address
shown in my profile.)
i know of a couple other resources, developed with reference to mathml, but
i don't have the links conveniently to hand. i will update this when i
.texdocument if you use XeTex or LuaTex, cf. tex.stackexchange.com/q/34604/34551 To answer your question, you can also rely on off-line service as a good old pdf cheatsheet.