Correct, the H is for HSPA. Since it's a Verizon variant, it's most likely programmed to show 1X for 1xRTT, 3G for EDVO, and 4GLTE for LTE since those are the technologies used by Verizon. The Technologies used by AT&T (E for EDGE, H for HSPA {though an AT&T variant should indicate this with 4G}) will likely revert to how they're handled in AOSP since Verizon users wouldn't normally encounter these types of networks. However it will likely still show 4GLTE if on LTE. When Verizon launched LTE and Sprint launched WiMax, AT&T and T-Mobile didn't want their networks to sound inferior to Verizon and Sprint, so they branded HSPA as 4G even though it's more like 3.5G due to pathetic upload speeds and ping times.
If it's showing H, then it must be AT&T or T-Mobile's network because they're they only carriers with an HSPA network in the US.