How to change 'Your Name'?

You can accomplish this using a case modification parameter expansion of $USER instead of \u inside the PS1 environment variable. The expansion would be ${USER^} to uppercase only the first letter of the username).

You can run this variable assignment on the terminal to see the effect:

PS1='\[\e]0;${USER^}@\h: \w\a\]${debian_chroot:+($debian_chroot)}${USER^}@\h:\w\$ '

If do you want to make this change permanent, you can use this method:

1. Edit the .bashrc file in your home folder

2. Locate these lines:

   if [ "$color_prompt" = yes ]; then
       PS1='${debian_chroot:+($debian_chroot)}\[\033[01;32m\]\u@\h\[\033[00m\]:\[\033[01;34m\]\w\[\033[00m\]\$ '
   else
       PS1='${debian_chroot:+($debian_chroot)}\u@\h:\w\$ '
   fi
   

3. In the two lines that begin with PS1=, replace \u by ${USER^}, so it looks like this:

   if [ "$color_prompt" = yes ]; then
       PS1='${debian_chroot:+($debian_chroot)}\[\033[01;32m\]${USER^}@\h\[\033[00m\]:\[\033[01;34m\]\w\[\033[00m\]\$ '
   else
       PS1='${debian_chroot:+($debian_chroot)}${USER^}@\h:\w\$ '
   fi