Using the AKC name Checker you can use Nicolas Koda Reigan Höllenhund for the official name.
This is the name checker website that may help you as you can change the order for the name: http://www.akc.org/reg/namingofdog.cfm
They will allow you to use 36 characters for the name and if you add more they charge $10.00 The site goes over the number of characters for naming the puppy.
The papers will include sire and dam listed on them.
Would there not be an Von or a Der in between and if so how would it look
Nicolas Von Koda Der Reigan Höllenhund.
Also who comes first the Mother or the father in German?
Yes you could use Nicolas Von (of) Reigan und (and) Koda Höllenhund.
The word Der means The. You would want to use UND (and) meaning of Dam and Sire.
This would be using the Dam's name first and the sire. There is no set way of doing this as you see below from one of my AKC registrations.
You can check the allowance of the name on the link I included above. When My dogs have been registered the breeder had used the Name Von dam and sire and breeders name. It can be changed to as long as the AKC gives approval to the name being used.
I pulled out some of my AKC registrations and this is the way it is written:
JLG's Lady Fearless of Billo
German Shepard Dog
Black and tan
DW's Theodore Bear Of Billo
Warrens Lady Shy of Billo