According to Kunitzsch the earliest use of the name Regulus appears to be by
Johannes Werner (1468-1528) in his work _De motu octaue sphaerae tractatus
primus_, included in _Libellus Ioannis Verneri Nuremburgen, super
vigintiduobus elementis conicis_ (Nuremberg, 1522).
The name Regulus was also used by Petrus Apianus (1495-1552) in his
_Cosmographicus Liber_ (first edition publ. in 1524, Landeshut & Antwerp)
and in his _Horoscopion Apiani generale_ (Ingolstadt, 1533).
Also in the 1528 edition of the Almagest translation completed in 1451 by
Georgius Trapezuntus (_Claudii Ptolemaei Pheludiensis Alexandrini Almagestum
seu Magnae Constructionis Mathematicae Opus_, Venice, 1528).
You can find details in
Paul Kunitzsch, _Peter Apian und Azophi: Arabische Sternbilder
in Ingolstadt im frühen 16. Jahrhundert_ (Munich, 1986 [=
_Sitzungsberichte der Bayerische Akademie der Wissenschaften_,
Philosphisch-Historische Klasse, Jahrgang 1986, Heft 3]),
pp. 53-56 [Exkurs III].