Is dealcoholized wine completely alcohol-free?

Unfortunately, there are no standard regulatory definitions on what terms constitute what alcohol content. The term alcohol-free in the USA means 0.0% abv, but in the UK it means <0.05% abv, and for the EU its <0.5% abv. The term non-alcoholic, in the USA is <0.5% abv, whereas in Australia it is 0.0% abv. But in general, it can be expected that some trace of alcohol remains although small, and most products add the alcohol content to their labels.