Since no one else seems to have answered so far:
Afaik, there is no way to read that value. Since you set it in the component, there might be a define or constant referring to it in the BLE component generated files. I would suggest reading through there, but otherwise I don't have any tips on where or if it is located in those files.
Thanks for the response. I made a quick search and found nothing resembling. Maybe cypress will give access in the future.
Try looking at the beginning of the BLE_gatt.c file that is generated, it seems to be putting hardcoded values that reflect the name and DB as configured by the component editor on the top design schematic. The structure of interest appears to be called: CYBLE_GATTS_ATT_GEN_VAL_LEN_T cyble_attValuesLen[CYBLE_GATT_DB_ATT_VAL_COUNT]
It has accurate length values declared in my project, let me know if this has accurate values for yours and works for you.