Ok I'll take a run at it.
At a dterm in sequence and without pauses press TRF, CNF, *, TRF, CNF, #
After this you should see CAT MODE displayed. If not you either didn't do the sequence fluidly enough or the dterm is restricted from programming.
If you have a password on your system the next job is to enter it. To do this press LNR/SPD and you should see COMMAND= dial 03 then press RECALL the display should go to 03> now it gets tricky as you need to know what level your password is. If it is the high level password you would now dial 7 then press RECALL. If you do this and the display shows CODE NOT USED then you don't have to worry further. if you get a dash after the seven you enter the password then press CNF. If you are unsure of the level of your password you can work your way down from 7 to 0
If there is a password and you don't know it your vendor is legally obliged to give it to you and they can't charge for that. If you can't get it that way NEC can crack the password for you but please don't ask anyone here to tell you how to do it yourself.
So assuming we have got past the password bit press LNR/SPD to get the COMMAND= prompt dial 770 and press RECALL then dial your first station number and press RECALL this should display the current setting with a dash after it the dash means you can enter data if you want. It now gets hard again as in this command the names are entered using hexadecimal code. There is a simple way of finding the code for each letter if you have a manual as a conversion table is given. If you don't have this you can create one in excel using the instructions given here
When you have entered the code press CNF and thats it you have just changed your first name.if you want to view your handiwork just press RECALL and it will display the new setting.
If you want to continue in sequence you can step on to the next extn number by pressing SPKR
If you want to do another out of sequence press ANS and then dial in the station number followed by RECALL again.
All these changes are held in volatile memory so before you exit programming mode you need to back it up to flash rom to do this press LNR/SPD to get the COMMAND= prompt then using the line keys on the dterm counting the top left as A counting from left to right and top down enter EC (so that is the fifth and the third line keys) then dial 6 and press recall the display should look like this EC6>
now dial 0 and press RECALL and you should see EC6>:3-
dial 0 press CNF and that is the data saved (it actually takes a minute or two) in fact if you press RECALL it will display a 1 instead of a 3 which means now saving. You can only press the RECALL once here to see if it is writing if you want to look again press ANS dial 0 and press RECALL again each time you want another look when you see 3 again the save is complete but you don't need to keep looking as once you set it going you can forget it.
When you have finished simply lift the handset and put it back down.
one note here the CNF key is also known as EXE for execute and once you press it you have written the data so if you are unsure and haven't yet pressed it just lift the handset and hang up to get out.
Good luck hope this helps.