Steppe Grey Shrike** (whose status over the decades has swung between species and subspecies) characteristically occupies desert, saxaul desert or dry rough ground, & not steppe-like grassland as a migrant breeder (Panov & Bannikova 2010), thus the English name Saxaul Grey Shrike is inadequate.
Currently, it is a subspecies (IOC11.1) within the Great Grey Shrike Lanius excubitor complex, but molecular research so far carried out indicates its closest relative in that complex is the largely sedentary lahtora of the Indian subcontinent, just reaching easternmost Iran, which taxon has priority (Olsson et al 2010) (Some have called lahtora + pallidirostris Desert Grey Shrike, but that name has been used earlier for the African taxon elegans.
The OSME Region List names this combination 'Mauryan Grey Shrike', because its distribution matches that of the greatest extent of the Mauryan Empire (also called the Mahajanapada Federation). Possible other English names are 'Mughal Shrike' or 'Timur Shrike'.
Dutch Birding group lahtora + pallidirostris + aucheri + buryi as 'Asian Grey Shrike'.
MJB
**The name Steppe Grey Shrike has also been used earlier, but for L.(e.) homeyeri (Dement'ev & Gladkov 1968).
Dement'ev, GP and NA Gladkov. 1968. Birds of the Soviet Union. Vol 6. Israel Program for Scientific Translations, Jerusalem. [English translation of the 1954 Russian original: Ptitsy Sovetskogo Soyuza. Sovetskaya Nauka, Moscow.]
Olsson, U, P Alström, L Svensson, M Aliabadian and P Sundberg. 2010. The Lanius excubitor (Aves, Passeriformes) conundrum—Taxonomic dilemma when molecular and non-molecular data tell different stories. Mol. Phyl. & Evol. 55(2): 347-357.
Panov, EN and AA Bannikova. 2010. On the validity of the 'Steppe Grey Shrike' as an independent species. Sandgrouse 32(2): 141-146.