I think it's really difficult to find a good middle name for it. For example take your combo Tru
Elizabeth - say it out loud. I always go Tru
Elizabeth? as opposed to fake
Elizabeth? So I prefer it as a middle name. My favorite combo is
Adelaida True, nn
Ada. I prefer True over Tru.
Some celebrity has a daughter named True Harlow. I think it works with an unusual middle name. I really like True Harlow a lot. With an unusual middle name you are not likely to think Tru
Elizabeth as opposed to fake
Elizabeth because the name is so unheard of that you don't associate it with a person, if that makes any sense.
Some more
True
HarperTrue Marlow
True
NoelleTrue
Calista
something like that
True
Chrysanthe works as well.