My great grandfather from South Africa took a knife and fork set from a German soldier during World War II in Italy. On the back of the knife with the swastika symbol there is a number ...7001519 engraved. Does this number belong to a specific soldier and can I get a name or any other information regarding this?
Wehrmacht soldiers had indeed a unique identification number. It’s the number engraved into the ''Erkennungsmarke'' (“dog tag”). The number usually consists of the abbreviation of the unit in which the soldier first served (''Truppenteilbezeichnung'') and a running number. See an example at Wikimedia Commons. A list with of these numbers (''Erkennungsmarken-Verzeichnisse'' or EM-Verzeichnis'') is kept at ''Deutsche Dienststelle'', a part of the German national archives. When the remains of a soldiers are found, he can be identified this way.
The number on the cutlery in your possession doesn't match this kind of number. It's probably more of an inventory number that doesn't allow any conclusions to be drawn about the soldier.
If you like, you can add a photo of the cutlery to your question. Maybe there is an expert who can tell us more about it.