Possibly named after Russian exiles who lived round there after the revolution.

However, the theory re Russian exiles is disputed / unproven. The Exiles club was a house club belonging to Cable & Wireless which had an existence in Malta long before the Russian exiles arrived. This club had a beach hut built at the Exiles. A few Russian exiles who were present in Malta for a few months would probably not have had enough physical presence to influence a name change to a particular part of beach in Malta. Conversely, C&W and hence the Exiles Club, was here in Malta for easily a 100 years, built a beach hut or changing room and used it continually. (C&W also had a submarine cable running from their HQ in St Julian's across the bay, surfaced at the Exiles and further to their Offices in Valletta). (Thanks to Patrick Caruana Dingli for the info).