Name Entity Disambiguation is the Natural Language Processing task of identifying textual records corresponding to the same Named Entity, i.e. real-world entities represented as a list of attributes (names, places, organisations, etc.). In this work, we face the task of disambiguating companies on the basis of their written names. We propose a Siamese LSTM Network approach to extract -- via supervised learning -- an embedding of company name strings in a (relatively) low dimensional vector space and use this representation to identify pairs of company names that actually represent the same company (i.e. the same Entity). Given that the manual labelling of string pairs is a rather onerous task, we analyse how an Active Learning approach to prioritise the samples to be labelled leads to a more efficient overall learning pipeline. With empirical investigations, we show that our proposed Siamese Network outperforms several benchmark approaches based on standard string matching algorithms when enough labelled data are available. Moreover, we show that Active Learning prioritisation is indeed helpful when labelling resources are limited, and let the learning models reach the out-of-sample performance saturation with less labelled data with respect to standard (random) data labelling approaches.