Most parents with triplets have them due to Assisted Reproductive Technology; the rate of spontaneous triplets is quite low but not at all age-dependent.
And most parents of triplets who are "in the last trimester" are gearing up for the arrival of premature, sick babies, since the average gestational age at delivery is 32 weeks.
Congratulations! Lots of great suggestions already, so here are few threesomes that sound like sibling combinations, nothing cutesy.
Audrey Cecilia, Corinne Susanna, Elise Rebecca (These could all be switched around, Cecilia Audrey, etc.)
Marion, Frances, Elinor
Beatrice, Eleanor, Harriet
Annabel, Louisa, Rosalie
Eloise, Phoebe, Vivien
We have a friend who is a triplet, and he always jokes he was "the lucky one" because one of his brothers is severely developmentally delayed and the other is hearing impaired. His parents did IVF to get pregnant because they were in their mid 40's.
Congrats! All of these names are below #400 on the SSA name chart (except Alessandra, which is #397), so I hope there not too popular to suggest.
Some combos that I think fit well together:
Alessandra, Francesca, & Gwendolyn
Erica, Bridget, & Lucille
Cynthia, Teresa, & Rosalie
Marlene, Edith, & Corinne