Named entities (NEs) are among the most relevant type of information that can be used to properly index digital documents and thus easily retrieve them. It has long been observed that NEs are key to accessing the contents of digital library portals as they are contained in most user queries. However, most digitized documents are indexed through their optical character recognition (OCRed) version which include numerous errors. Although OCR engines have considerably improved over the last few years, OCR errors still considerably impact document access. Previous works were conducted to evaluate the impact of OCR errors on named entity recognition (NER) and named entity linking (NEL) techniques separately. In this article, we experimented with a variety of OCRed documents with different levels and types of OCR noise to assess in depth the impact of OCR on named entity processing. We provide a deep analysis of OCR errors that impact the performance of NER and NEL. We then present the resulting exhaustive study and subsequent recommendations on the adequate documents, the OCR quality levels, and the post-OCR correction strategies required to perform reliable NER and NEL.