Matching place names across writing systems is a persistent obstacle to the integration of multilingual geographic sources, whether modern gazetteers, medieval itineraries, or colonial-era surveys. Existing approaches depend on language-specific phonetic algorithms or romanisation steps that discard phonetic information, and none generalises across script boundaries. This paper presents Symphonym, a neural embedding system which maps toponyms from twenty writing systems into a unified 128-dimensional phonetic space, enabling direct cross-script similarity comparison without language identification or phonetic resources at inference time. A Teacher-Student knowledge distillation architecture first learns from articulatory phonetic features derived from IPA transcriptions, then transfers this knowledge to a character-level Student model. Trained on 32.7 million triplet samples drawn from 67 million toponyms spanning GeoNames, Wikidata, and the Getty Thesaurus of Geographic Names, the Student achieves the highest Recall@1 (85.2%) and Mean Reciprocal Rank (90.8%) on the MEHDIE cross-script benchmark -- medieval Hebrew and Arabic toponym matches curated by domain experts and entirely independent of the training data -- demonstrating cross-temporal generalisation from modern training material to pre-modern sources. An ablation using raw articulatory features alone yields only 45.0% MRR, confirming the contribution of the neural training curriculum. The approach naturally handles pre-standardisation orthographic variation characteristic of historical documents, and transfers effectively to personal names in archival sources, suggesting broad applicability to name resolution tasks in digital humanities and linked open data contexts.