Rein or Giel

I think both are pretty cool. You could also spell Giel as Chiel, maybe you'd like that better? You could also name your son Rein and use Giel as a middle name, as a family name. But I like both of them, and I wouldn't know which one I like better.
If you need other options, here are some ideas:
Reinder Reinier Ries Rink Chiel Chaim Rijk Wout Tijn Gijs Feike Tije/Theije/Theye/oid Ties Teun Rens Siem Faas Guus Siem Sijmen Tijmen Noud/Naud/Naut Roef Roel Boet Loet

No wrong names, but I do have clear associations with the names. Not sure if you're from the Netherlands?
Rein (as in the Rhine > river and rein > pure)
Giel (Giel Beelen, radio DJ)
I'd rather go for Chiel or Machiel.

I really think Rein is lovely

I think the addition of Reinder is quite nice. I know a Giel, someone I had absolutely nothing to do with... so I associate the name with someone I know... which obviously doesn't work.
Your feeling about Rein... I tend to think of Reynard the Fox... such an old book...
Reinder feels a bit more cool... But hey... it's so personal... choose what feels right to you! What do you imagine calling out through the whole neighborhood when he needs to come for dinner?!? Good luck!