Beta Aquilae II
Beta Aquilae II was the inhabited second planet in its star system. The Beta Aquilae II Starfleet Academy annex was located there. 

This planet was named in the personnel file of Lois R. Eckridge, who graduated from the Academy on stardate 42091.0. (, okudagram)

Appendices

Background information
In the real world, Alshain is the traditional name of the  star system (and as of 2016 the official name of Beta Aquilae A, the system's primary star), but while Alshain IV appears in , the two names have not been connected in Star Trek canon.

According to Star Trek: Star Charts ("United Federation of Planets I") and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), the Beta Aquilae (Alshain) system was located in the Alpha Quadrant. It was a binary star system consisting of a Class G star and a Class M star.

In the pre-remastered "Eye of the Beholder", Eckridge was born on this planet. Her planet of origin was changed to Psi Epsilon IV for the remastered episode.
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Beta Aquilae 02