Congratulations, USA

No, we're either keeping our names or changing to Rivers so the kids have a simpler name than Parish-Rios or Rios-Parish or the connotation of only being 'one of ours'.

Don't foster children keep their names?
Or was the newspaper quote inaccurate and you are planning to adopt, not foster?

I approve of not going for a hyphenated name, though personally I'd probably prefer something like Parios or Paris, a combination of both your maiden names.