Knowledge extraction from symbolic data often produces abstractions that are formally defined but not immediately interpretable by users. Formal Concept Analysis (FCA) and Relational Concept Analysis (RCA) provide representative settings for this issue: they generate explicit conceptual structures, implications, and relational dependencies from object descriptions and relations. Although these structures are explainable by design, their concepts are often identified by technical labels, which limits their use as human-interpretable knowledge units. Assigning meaningful names to such concepts is therefore a key issue for interpretation, navigation, validation, and reuse by domain experts. This paper investigates concept naming in FCA and RCA from a symbolic knowledge representation perspective. We first characterize the linguistic and terminological challenges involved in naming generated symbolic abstractions, including ambiguity, discrimination, concision, and consistency across related concepts. We then propose a configurable framework for LLM-assisted concept naming. The framework relies on a variability model that controls which sources of information are exposed during naming, such as intent, extent, inherited information, neighboring concepts, implications, and relational attributes. It thereby makes explicit the semantic choices involved in moving from formal concept descriptions to human-readable names. The approach is illustrated as a proof of concept on a small relational dataset in the pizzeria domain. This illustration shows how different configurations influence the names suggested by an LLM, and how naming variability can reveal interpretation choices, relational dependencies, and possible modeling issues in the underlying symbolic data.