Legendary Resistances are available to you while Shape Changed
The appropriate part of the spell description says:
Your game Statistics are replaced by the Statistics of the chosen creature, though you retain your Alignment and Intelligence, Wisdom, and Charisma scores You also retain all of your skill and saving throw Proficiencies, in addition to gaining those of the creature, If the creature has the same proficiency as you, and the bonus listed in its Statistics is higher than yours, use the creature’s bonus in place of yours. You can’t use any legendary Actions or Lair Actions of the new form.
Legendary resistances are not mentioned anywhere as being unavailable or altered in anyway.
This is backed up by a (unofficial Tweet) tweet from Jeremy Crawford:
So you get Legendary Resistances?…
No rule says you don’t.