I can see H & M choosing Alice, after Princess Alice of Battenburg, Prince Philip's mother, who was hospitalised for MH reasons (was diagnosed with schizophrenia in 1930), upon release sheltered Greek Jews during the Holocaust and ended up as a Greek Orthodox nun. She was also congenitally deaf.
I love Eleanor and Rosa as suggestions. Also Helena, which is gorgeous imo. I could see Alexandra or Adelaide or Victoria too.
However, I would say they might go off piste altogether and choose something along the lines of Mia, Isla or Savannah.
Or maybe something popular but not royal - Isobel, Lily, Violet, Amelia.
No idea at all about boy names. Most likely not Thomas.