I would use "double contraction" which sounds more clear
Suffix-Prefix Double Contractions: suffix-prefix double contractions are formed from two contractions where the suffix of one contraction is the prefix of the other:
she + would + have = she'd + would've = she'd've
she + would + have = she'd + would've = she'd've
Prefix-Prefix Double Contractions: prefix-prefix double contractions, are formed from two contractions that share a prefix:
they + will + have = they'll + they've = they'll've
they + will + have = they'll + they've = they'll've
Peculiar Cases: double contractions where one of the contractions isn't arrived at formulaically makes the double contraction peculiar:
he will not = he'll not = he'lln't
he will not = he won't = he'on't
he will not = he'll not = he'lln't
he will not = he won't = he'on't
