Dolphie and IJsbrand have been able to trace the name Wiltens back to 1635, to a Gillis Maertensz Wiltens. (You can read more about this in the History.)
Our family name originated at the time when Albertus Jacobus had passed away and his widow Anna van Bijlandt remarried Johann Frederich Andrée.
Albertus and Anna had two sons: Gerard Adriaan and Martinus Pieter.

The latter adopted the name Andrée at his marriage, but placed it after Wiltens, so he continued to live as Wiltens Andrée.
All three of his sons died young, so that name did not get passed on. He did have daughters, but well, they don't count for passing on the name!

Gerard Adriaan did not adopt the name Andrée.
He was only 12 years old when his mother remarried; perhaps he didn't get along very well with his stepfather?
But when he had a son with Helena Bongé, he named him at the baptism:

Johan Frederik Hubert Andrée Wiltens.

I find this very strange: you are called Wiltens yourself, your brother calls himself Wiltens Andrée, and then you give your child the name Andrée Wiltens??

And it turns out this is not a spelling error by the civil registry, as evidenced by the fact that his little brother Albertus Jacobus is also named Andrée Wiltens.
Unfortunately, that child also died young.