4 of the 9 carriers here run their own network, and 5 rent space on one. ahamo runs on docomo, povo runs on au (KDDI), LINEMO runs on SoftBank, Y!mobile runs on SoftBank and UQ mobile runs on au (KDDI). A carrier that rents a network often has its own APN, so copy the one on its card, not the host's.
au (KDDI), SoftBank, LINEMO, Y!mobile and UQ mobile use a username and password in the APN. For the others, leave both fields empty: a username where none is needed can stop data from working. Where an authentication type is given: au (KDDI) uses CHAP, LINEMO uses CHAP, Y!mobile uses CHAP and UQ mobile uses CHAP.
SoftBank and Y!mobile list separate settings for picture messages (MMS). If texts work but photos in messages do not, those are the values to check. au (KDDI) and SoftBank also have a second APN for some plans or devices, shown on their cards.
The carriers here use the mobile country code 440, the first three digits of every network code in Japan. Android usually fills in the MCC and MNC from the SIM, so you rarely need to type them.
Visiting Japan with your own SIM? Keep your home APN: roaming data still goes through your home carrier. You only need these settings with a local SIM bought in Japan. Or skip the SIM shop with a Japan eSIM, which sets its own APN.