The traditional names of the Latin and Greek letters are used for unmodified symbols.
Examples: Note The IPA standard includes some small capital letters, such as ʀ and ɢ, although it is common to refer to these symbols as simply "capital" or "cap" letters, because the IPA standard does not include any full-size capital letters.
Note that ŋ is called eng or engma, ɱ meng, and ꜧ heng.
When the tail loops over itself, it's called curly: ʝ curly-tail j, ɕ curly-tail c. There are also a few unique modifications: ɬ belted l, ɞ closed reversed epsilon (there was once also a ɷ closed omega), ɰ right-leg turned m, ɺ turned long-leg r (there was once also a long-leg r), ǁ double pipe, and the obsolete ʗ stretched c. Several non-English letters have traditional names: ç c cedilla, ð eth (also spelled edh), ŋ engma or eng, ə schwa (also spelled shwa), ǃ exclamation mark, ǀ pipe.
Other symbols are unique to the IPA, and have developed their own quirky names: ɾ fish-hook r, ɤ ram's horns, ʘ bull's eye, ʃ esh (apparently never 'stretched s'), ʒ ezh (sometimes confused with yogh), ɧ hook-top heng.
This latter name is derived from its original form as a dotless question mark in a fashion reminiscent of gelding.