On the map, there only seems to be one Strait of Hormuz, and I'd say about 50% of the time, I have indeed heard it referred to as the 'Strait of Hormuz', but the other half of the time people will refer to the 'Straits of Hormuz'. Is this an arbitrary, incorrect pluralization? If so, how did it originate?
In general, the plural form seems to be preferred in most descriptions of narrow waterways connecting two large stretches of water. The OED has this note in its entry for strait:
When used as a geographical proper name, the word is usually plural with singular sense, e.g. the Straits of Dover , the Straits of Gilbraltar (formerly †the Straits of Morocco ), the Straits of Magellan , the Straits of Malacca , and the Straits as short for any of these; with regard to Bass('s) Strait(s) , Torres Strait(s) , usage is divided, while Davis Strait rarely appears in the plural form. The use of the plural for the singular began in the 15th c. A few writers, chiefly of gazetteers, use the singular consistently throughout.
It may not be as much as half the time that people refer to it as the 'Strait s of Hormuz'. A majority of standard references seem to refer to it correctly in the singular.
One possible source of the sudden popularity in recent times could be Johnn Schroeders' March, 2011 book 'Straits of Hormuz', and propelled by current geopolitical interest in the region.