•Brand awareness-quality inference affects negatively the consumer-SB identification.•The more aware consumers are of a brand the greater the perceived risk in the SBs.•Perceived risk is a decisive factor of the drivers of SB identification.•Differences in the modelling proposed are shown for quality consciousness.•Investment in brand awareness is necessary to expand customer base of SBs. Store brands (SBs) have currently become consolidated in the food market, have achieved an objective quality similar to that of manufacturer brands and a competitive price. However, food retailers have invested little in communication about these brands, considering it enough to use proximity to the consumer and economies of scope derived from the presence of their own brands throughout the establishment. This paper explores the consequences of this communication strategy about SBs on the functional risk perceived by consumers for these brands and the consumer’s identification with them. We propose a theoretical model, contrast it empirically for food products, and perform a multigroup analysis of quality conscious and non-quality conscious consumers. The results obtained reveal a negative effect of the inference brand awareness–brand quality on the consumer’s identification with the SB as a result of the greater functional risk perceived for these brands. This effect is substantially greater in quality conscious consumers, a key segment for retailers since it constitutes the target of their premium SBs. The results show retailers that investment in communication of SBs is absolutely necessary to dismiss SB functional risk and expand customer base by appealing to quality conscious consumers. The investigation has significant implications for the retailer’s strategy for marketing SBs in food products.