Abstractive text summarization (ATS) is both important and challenging. Recent studies have shown that ATS still faces various forms of hallucination. Our study also indicates that a significant portion of hallucinations is named entity-related. They might appear in different forms, such as mistaken entities and erroneous entity references. The underlying causes implicit in data are complex: data samples pose varying learning conditions. Despite recent research efforts dedicated to named entity-related hallucinations, the solutions have not adequately addressed the varying learning conditions posed by data. This paper aims to bridge the gap in pursuit of reducing intrinsic named entity-related hallucinations. To do so, we propose an adaptive margin ranking loss to facilitate two entity-alignment learning methods to tackle them. Our experiment results show that our methods improve the used baseline model on automatic evaluation scores. The human evaluation also indicates that our methods jointly reduce the intrinsic named entity-related hallucinations considerably compared to the used baseline model.