Looks like the atmega328 (without the P) isn't in the config file for avrdude. Locate file avrdude.conf, open it in an editor and locate the atmega328p section, which starts like this:
#------------------------------------------------------------
# ATmega328
#------------------------------------------------------------
part
id = "m328p";
desc = "ATMEGA328P";
has_debugwire = yes;
flash_instr = 0xB6, 0x01, 0x11;
eeprom_instr = 0xBD, 0xF2, 0xBD, 0xE1, 0xBB, 0xCF, 0xB4, 0x00,
0xBE, 0x01, 0xB6, 0x01, 0xBC, 0x00, 0xBB, 0xBF,
0x99, 0xF9, 0xBB, 0xAF;
stk500_devcode = 0x86;
# avr910_devcode = 0x;
signature = 0x1e 0x95 0x0F;
If you change the final signature byte from 0x0F to 0x14 then it should recognise your chip (but not a atmega328p). Or you could try copying the whole atmega328p definition and in the copy change the id, desc and signature byte fields, then use the new id or desc to identify the chip in boards.txt, but I don't know whether this works.