Scientific names for organisms are also known as Latin names. Carl Linnaeus (pictured) started the naming scheme used in biology to today, with a few modifications. At the time, Latin was still a fairly dominant language of scholarship. So Linnaeus gave plants, and later animals, names in Latin. I think names based on Greek are also acceptable.
Today, for animals, the rules for names are handled by the International Commission on Zoological Nomenclature (ICZN). There are similar but separate organizations for plants and microbes and, I believe, fossils.
I'm going to do my best to summarize other people's arguments about giving Marmorkrebs a scientific name. (Some of these are based on half-remembered conversational snippets from conferences, so forgive me if I make errors.)
Marmorkrebs seems to belong in the genus Procambarus. The major crayfish taxonomist who described many of the members of this genus was a man with the wonderfully alliterative name of Horton H. Hobbs, Jr.. He based many of his species descriptions on the basis of the male sex organs... which Marmorkrebs, being all females, do not have.
The next plan of attack might be to use genetics. But there really isn't a lot of precedent for describing species on the basis of genes alone. I am not sure whether the ICZN code allows it. Regardless of whether it is permissible, there are strongly established traditions in taxonomy, and formal species descriptions are supposed to have detailed morphological descriptions, designate a type specimen for safekeeping in a museum, and so on.
And as you consider the problem of whether to give Marmorkrebs a scientific name, it leads to a very core question: What is a species? This is a question that has resulted in a lot of ink being spilled in scientific papers, and simply put, there is no consensus on how to define a species.
Based on some comments Keith Crandall has made, Marmorkrebs are genetically extremely similar Procambarus alleni... so following some species concepts that revolve around morphological separation, this might qualify as putting Marmorkrebs in with P. alleni.
But because Marmorkrebs reproduce asexually, they do not interbreed with sexual species... so following species concepts that revolve around interbreeding, this would suggest that Marmorkrebs should get its own species name.
As the preface to the latest edition of the code of zoological nomenclature notes:
One should always keep in mind that an important function of classifications is information retrieval.
So maybe it's not really critical to have a scientific Latin name immediately in these days of search engines and databases... but what is definitely important is to have a consistent name, one that can be found in databases.
For obvious reasons, I suggest "Marmorkrebs" be that name for use in titles and keywords.