(You gotta love these type of cases, no one else will.)

Mom uses minor son's ssan to open utility account. (Has never had custody of the child.)

Mom does not pay utility bills and son (eight year old) now has utility company writing letters about non payment. (This has been fixed by utility company.)

Mom has stolen ID. (I think.) Is she also guilty of theft? (For the utilities used.)

If it happened after 9/1/07, you might could get her for PC 32.51, Fraudulent Use of Identifying Information -- the legislature just removed the "no consent" element when the victim is under 18yoa to address precisely this type of parental malfeasance.