A context menu operation will be platform-specific, and I don't
think you mentioned your platform(s). On MacOS, I used to use
https://earthlingsoft.net/UnicodeChecker/ (which also does HTML entities).
If you're OK with a command line tool, I just finished updating and finally publishing a Python script I wrote for that purpose around 15 years ago: https://pypi.org/project/unicode-name-inquiry/ Lots of options, but default usage is, for example:
$ uni ≥
≥ U+2265 GREATER-THAN OR EQUAL TO
(It doesn't currently do the string-of-symbols case, because it tries to interpret strings as some other character identifier, e.g. `uni tilde` or `uni 8805`, but that sounds like a reasonable option to add.)
Typically, people just search for the character on the web and land on one of the many ‘monetized code charts’.