For package shapes/names I would recommend using manufacturer names. This is much safer than coming up with descriptive names like QFN32_5x5 as there are multiple 5mm 32Pin QFN shapes even when pitch is the same, this makes it safer to use a name in the form Manufactuer_PackageCode e.g TI_PDG-6 (I made that one up but you get the idea).
SOIC are usually much more standard as long as you make sure you use the right names in the TSSOP/MSSOP/SSOP range then you can just call those SSOP28 etc. Good old 1.27mm pitch IC's come in 3 basic widths so thats SO16 for narrow, SO16W for wide and SO16M for the rather rare in-between size for example. Be aware that the package name included in CAD data or Digikeys page is often gibberish, always check it. For chip type parts you might want to include a height parameter in the name e.g C0805-1.2 for particularly big chunky caps for instance. However if your machine has for feedback it might not really care about minor height variations like that.
For part number I would suggest you use your internal part number. That way if purchasing changes manufacturer or whatever, kitting/stores and your MRP handles it, not your production line operator.
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