If you have Windows 95, download and install the latest Dial Up Networking upgrade from Microsoft. You must also have Client for Microsoft Networks installed. Go to Start, Settings, Control Panel, Network. If you do not have Client for Microsoft Networks installed, go to Add, Client, Add, on the left go to Microsoft, on the right to to Client for Microsoft Networks, Ok, then OK, and restart your computer. Next time it starts, your computer will ask for a name and password, put in a name, but not a password, and confirm that you do not want a password. You should now be able to save your internet password.
Refer to Microsoft article Q137361 for more help.
Also, article Q148925 provides more information if saving your password does not work.
Links to more information:
User Name Keeps Changing in Dial-Up Networking Connection
User Information Not Saved for Dial-Up Networking Connection