The full name (or the name of his teacher?) is Stag phu Bla ma Blo bzang bstan pa'i rgyal mtshan.
Bibliography:
Byang chub sems kyi sems mnga' ba'i bya mgrin sngon zla ba'i rtogs pa brjod pa 'khor ba'i mtha' dag la snying po med par mthong ba rnams kyi rna rgyan.
A xylograph from the Bacot collection, also owned by the Library of the School of Oriental Studies (London), in 133 folios. See E. Conze, The Buddha's Law among the Birds, Motilal Banarsidass (Delhi 1996), p. 51. The author, a monk at 'Bras spungs, says he is just retelling a story told to him by his teacher Stag phug Bla ma Blo bzang bstan pa'i rgyal mtshan. Although Conze did not know it, the latter is a known personage, whose dates were 1714-1762 (a list of his collected works is available, and he was a Dge lugs pa, not a Bka' brgyud pa as Conze thinks).
A copy is found in the Nepal-German Manuscript Preservation Project microfilms (ID no. 220), where it is attributed to Stag phu Blo bzang bstan pa'i rgyal mtshan (b. ca. 1765), while the name of the author as given on the original card is Gnubs rigs Ban de Ma ti.
Tôhoku catalogue, no. 7051.
Deliash N. Muzraeva, The Tale of the Moon Cuckoo by Stag phu ba Blo bzang bstan pa'i rgyal mtshan and Its Spread in Central Asia, contained in: Per Kvaerne, ed., Tibetan Studies: Proceedings of the 6th Seminar of the International Association for Tibetan Studies, The Institute for Comparative Research in Human Culture (Oslo 1994), vol. 2, pp. 580-585.
Lama Lo-drö of Drepung, The Prince Who Became a Cuckoo: A Tale of Liberation, tr. & ed. by Lama Geshe Wangyal, Theatre Arts Books (New York 1982). Here the date of composition is given as 1857.