Neural encoders of biomedical names are typically considered robust if representations can be effectively exploited for various downstream NLP tasks. To achieve this, encoders need to model domain-specific biomedical semantics while rivaling the universal applicability of pretrained self-supervised representations. Previous work on robust representations has focused on learning low-level distinctions between names of fine-grained biomedical concepts. These fine-grained concepts can also be clustered together to reflect higher-level, more general semantic distinctions, such as grouping the names nettle sting and tick-borne fever together under the description puncture wound of skin. It has not yet been empirically confirmed that training biomedical name encoders on fine-grained distinctions automatically leads to bottom-up encoding of such higher-level semantics. In this paper, we show that this bottom-up effect exists, but that it is still relatively limited. As a solution, we propose a scalable multi-task training regime for biomedical name encoders which can also learn robust representations using only higher-level semantic classes. These representations can generalise both bottom-up as well as top-down among various semantic hierarchies. Moreover, we show how they can be used out-of-the-box for improved unsupervised detection of hypernyms, while retaining robust performance on various semantic relatedness benchmarks.