It’s label placement issues – at zoom levels 14-16 there are too many other symbols to fit the placename on.

Ideally we’d place the label further away when this happens, but unfortunately Mapnik (the rendering software) doesn’t cope very well with that and has a habit of repeating placenames in such circumstances. (That can even happen at smaller scales – see Bishop’s Castle and Church Stretton here, for example!) It’s something that affects all Mapnik-based maps to a greater or lesser degree, but cycle.travel is particularly affected because it tries to show icons earlier in rural areas – z13 compared to z16 on OpenCycleMap, say.