Science fiction readers will likely know of Alpha Centauri, which navigators call by its proper name Rigil Kentaurus, because this is the nearest star to our solar system and perhaps an early one to visit or receive visitors from.
Figure 1. Sample of star names. The red labels have been added. Selected stars called navigational stars are assigned  unique numbers in the Almanac.
Figure 2. Sample star chart from the Almanac.
Figure 3. Greek alphabet
Note on Constellations
We often think of constellations as groups of stars, but that is not the full picture. The full sky is divided up into sections with straight boundaries (SHA and Dec), much as a state is divided up into counties.  The full globe of the sky is divided into 88 constellations, which means that every point in the sky is in a constellation, even if there are no stars near it.  If you look up any constellation in the wiki it will include a nice vector image of the constellation boundaries. A sample is shown below.
Figure 3a. Outline of the constellation Ursa Major (white area).  See these for any constellation
in the wikipedia.
in the wikipedia.
Navigational Stars
There is yet another classification of stars that is crucial to navigators. The 57 stars listed on the daily pages are called navigational stars. They are also on the Index to Selected Stars in the back of the Almanac (p. xxxiii). These are bright stars, magnitude 1 or 2, but they are not chosen by brightness alone, but rather selected uniformly around the sky so that several of them will be in view at all times from any location. Polaris is notably not on that list, though it is used routinely for navigation and certainly qualifies as a "navigational star."
Figure 4. Index to Selected Stars—the navigational stars. 
This list has been on page xxxiii of the Almanac for many years, which is easy to remember, and it is also printed on the yellow cardstock bookmark that comes with the Almanac. Listing the stars by number and alphabetically is a handy feature of this list. Cel nav apps, including our own StarPilot, often use these star numbers for a quick way to select a star.
There are another 116 stars listed in the back of the Almanac that do not show up on the daily pages. That full list (174 stars) includes the navigational stars, and is presented in a unique manner, illustrated in Figure 4. The first half of the year (January to June) lists the stars by their Bayer designation ("Greek-letter name"), whereas from July to December they are listed by their proper names. This can be an important nuance to know when it comes to some star ID questions. All navigational stars have a proper name.
Figure 5. Sections of two facing pages of the star list at the back of the Almanac.
Here we learn, for example, that the brightest star in the sky, Sirius, is also known as Alpha Canis Majoris, the alpha dog in the Dog constellation. It has still another name—you guessed it: the Dog Star.
Stars in this list are sorted according to increasing SHA. If you know the star but not its SHA, check the star maps in the Almanac or the USNO version linked above, which plots star locations on a Declination-SHA grid.
This list provides more stars for navigation but it is very rare that we need one from this list. The navigational stars usually carry us across the ocean. Indeed, any ocean can typically be crossed using the same few stars with the aid of a planet or two. See a real example in Hawaii by Sextant.
 How to Pronounce a Star's Name
My answer would be, just about however you want to.  These are often complex names; many evolved from the Arabic, although Arabic speaking persons might not recognize the present form of the word. Alnilam, Alioth, Altair, are examples, as is, by the way, Alcohol. In fact, many of the prominent stars have many names, or many spellings for the same name, although there is now an official list of names and spellings as of June, 2018.  You will see that most of these were only formalized in 2016 or 2017.The wiki has good presentations of stars organized by constellations, which include detailed maps of the constellation. Standard pronunciation guides are complex, so here is a starting point for the navigation stars, plus a few others we use in the course. There are more alternatives than I have listed here.
Name                Pronunciation
Acamar               AH-kuh-mar
Achernar             AK-er-nar
Acrux                A-krucks
Adhara               ad-HAR-a
Al
Nair              all-NAYR
Aldebaran            al-DEB-ah ran
Alioth               AL-lee-oth
Alkaid               AL-kade
Alphecca             al-FECK-ah
Alpheratz            AL-fer-rats
Altair               AL-tair
Ankaa                ANG-kah
Antares              an-TAIR-ease
Arcturus             arc-TOUR-russ
Atria                AH-tree-a
Bellatrix            BEL-la-trix
Betelgeuse           BET-el-jooz
Canopus              can-OH-pus
Capella              kah-PELL-ah
Caph                 KAF
Castor               CASS-ter
Deneb                DEN-ebb
Denebola             de-NEB-oh-la
Dubhe                DOOB-huh
Elnath               EL-noth
Eltanin              EL-ta-nin
Enif                 EEN-if
Fomalhaut            FO-mal-oh or FOH-mal-owt
Gacrux               GAK-kruks
Gienah               JEEN-ah
Hadar                HAH-dahr
Hamal                HAM-al or hah-MAHL
Kaus
Australis       KOWSS ow-STRAH-liss
Markab               MAR-kab
Megrez               meg-REZ or MEG-rez
Menkar               men-KAHR
Menkent              men-KENT
Merak                MER-ak
Miaplacidus          mee-a-PLASS-id-uss
Mintaka              MIN-ta-ka
Mirfak               MERE-fak
Mizar                MYE-zahr
Nunki                NUN-kee
Peacock              pea-COCK
Polaris              poe-LAIR-is or poe-LAHR-is
Pollux               POL-lucks
Procyon              PRO-see-on
Rasalhague           RAHS-al-haig
Regulus              REG-you-luss
Rigel                RYE-jel
Rigil
Kentaurus      RYE-jel ken-TAW-russ
Sabik                SAH-bik
Saiph                SAFE
Scheat               SHEE-at
Schedar              SHED-er
Segin                SEG-in
Shaula               SHOWL-a
Sirius               SEER-ee-us
Skat                 SKAHT
Spica                SPEE-ka or SPY-ka
Suhail               soo-HALE
Vega                 VEY-ga or VEE-ga
Zubenelgenubi        zoo-BEN-el-je-NEW-bee
Zubeneschamali       zoo-BEN-ess-sha-MAH-lee
My suggestion is choose a way to say it and then whenever you do say it, say it bold and clear. Anyone hearing who might have thought it was done another way would then pause, and likely take your word for it. It would be difficult in many cases to argue what is right.
For more, the definitive study of star names is the classic Victorian text Star Names Their Lore and Meaning by Richard Hinckley Allen, which is online, being a remarkable work of Bill Thayer, formerly of University of Chicago. There are also tons of used print copies online for a dollar or two, being the Dover edition from the early 60s. We have a copy of that one which we scanned, OCRed, and cleaned up to make an ebook long before Bill Thayer's work and also long before Google got into the practice of scanning all books.
The best stargazing program for Mac or PC is the amazing free one called Stellarium. Has a short learning curve, but is a remarkable and beautiful tool. You can read digital values of height and bearing for cel nav studies as well.







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