The small screens of smartwatches provide limited space for input tasks. Finger identification is a promising technique to address this problem by associating different functions with different fingers. However, current technologies for finger identification are unavailable or unsuitable for smartwatches. To address this problem, this paper observes that normal smartwatch use takes places with a relatively static pose between the two hands. In this situation, we argue that the touch and angle profiles generated by different fingers on a standard smartwatch touch screen will differ sufficiently to support reliable identification. The viability of this idea is explored in two studies that capture touches in natural and exaggerated poses during tapping and swiping tasks. Machine learning models report accuracies of up to 93% and 98% respectively, figures that are sufficient for many common interaction tasks. Furthermore, the exaggerated poses show modest costs (in terms of time/errors) compared to the natural touches. We conclude by presenting examples and discussing how interaction designs using finger identification can be adapted to the smartwatch form factor.