Basis of enzyme nomenclature — pyruvate dehydrogenase
The pyruvate dehydrogenase complex catalyses the oxidative decarboxylation of pyruvate. A description of this is easy to find on the web (e.g. Wikipedia), but I would recommend the section in Berg et al. Biochemistry (online), as it is an authoritative book with a high reputation.

Pyruvate + CoA + NAD+ → acetylCoA + CO2 + NADH

In the overall reaction, shown above, pyruvate is being oxidized (hydrogen removed) by NAD+, which is reduced to NADH. Hence there is nothing surprising in the enzyme having acquired the description, dehydrogenase.
Before asking questions about enzyme nomenclature, one should consider the historical and scientific context in which names arose. This was general scientific ignorance of the overall metabolic pathways in which they occurred or even the direction in which the reaction normally proceeded. There is also the question of focus — here on oxidation of carbohydrates. The working names that arise — trivial names, as they are called — tend to stick: they are in the literature and everyone in the field knows what you are talking about. Eventually, when the dust has settled, scientific commissions assign systematic nomenclature. In this case there are three enzymes involved, so that each has its own systematic name:

Pyruvate dehydrogenase (acetyl-transferring) — EC 1.2.4.1
Dihydrolipoyl transacetylase — EC 2.3.1.12
Dihydrolipoamide dehydrogenase — EC 1.8.1.4

It can be seen that even the systematic name for enzyme E1 (which catalyses the decarboxylation) does not refer to the decarboxylation, but to the transfer of the acetyl group (to thiamine pyrophosphate and then to lipoamide), which is of more interest mechanistically.
Details of the reactions and alternative names corresponding to the EC numbers  (Enzyme Commission numbers) can be found either on the Queen Mary University site or Expasy.