I recently changed my Minecraft username. Since I could not login to the server, when I was logging in, I used my regular name. I use the password that I always use, but it doesn't work.
If you mean the Minecraft Website: If you have a Mojang account, login with your e-mail instead of your username.
Try logging in with both usernames, old and new, making sure your password is correct if you are 100% sure you have a Minecraft account and NOT a Mojang one.
As a last resort, contact Mojang.
If you mean /login in a server: Like Antoine said in the comments, servers with /login are cracked and you shouldn't use them anyway. However, your login password should be the same.