Stability of α, β, γ allotropes at different temperatures
I think most of the time, they sort according to the order which temperature the allotrope/polymorph is more stable. Let's say element Z has two allotropes A and B. A is stable below 100 °C and B is stable above 100 °C. Thus allotrope A would be denoted alpha-Z and allotrope B would be denoted beta-Z.
Gray tin (alpha-tin) and white tin (beta-tin) is an example. Gray tin is stable only below 13.2 °C and white tin is stable above this point. So that's why gray tin is called alpha-tin because it is stable at a lower temperature, and ditto with white tin. As you can see in this case the beta allotrope would be the one stable at room temperature one.
Quartz (a crystalline form of silicon dioxide) is another example. See this from Wikipedia:

Quartz exists in two forms, the normal α-quartz and the high-temperature β-&gt;quartz, both of which are chiral. The transformation from α-quartz to β-quartz &gt;takes place abruptly at 573 °C (846 K; 1,063 °F).