What does γ mean before a gene name?
Yes, in this context $\gamma$ indicates phosphorylation. See e.g. &quot;The phosphorylated form of H2AX is called $\gamma$-H2AX [18, 19].&quot; from here, and references therein.
I am unsure of the exact basis of this, but I believe that it is because the gamma phosphate group of a nucleotide triphosphate is the one that is generally used by kinases to phosphorylate other functional groups. SEE UPDATE for derivation.
Other notations such as the $p$ prefix are more readable to me, but the usage appears to be cultural and somewhat field-specific.
Update
In response to @MattDMO comment, I read further and found that the terminology derives from this paper. They don't directly explain the terminology, but in context it's pretty clear:

At the maximum, approximately 1% of the H2AX becomes $\gamma$-phosphorylated per Gy of ionizing radiation.


In mammals, the serine in this motif is residue 139, the site of γ-phosphorylation.


When mammalian cell cultures are exposed to ionizing radiation and the acid-soluble nuclear proteins are analyzed on two-dimensional AUT-AUC gels, novel components that will be referred to as $\gamma$ (Fig. 1, A and B) are found in the H2A region of these gels.

It appears that the name probably derives from an observation that was just &quot;whatever in this 2-D gel is $\gamma$-P32 labeled when we induce DSBs when $\gamma$-P32 ATP is present.&quot;
@MattDMO also points out that the irradiation that induces the gamma component in this context is gamma radiation. So it's all a bit of a muddle, it could also be that.