Show only current directory name (not full path) on bash prompt

Change the \w (lowercase) to \W (uppercase):

PS1='${debian_chroot:+($debian_chroot)}\[\033[01;32m\]\u@\h\[\033[00m\]:\[\033[01;34m\]\W\[\033[00m\]\$ '
                                                                                       ^^
           this one waaaaaay over here ------------------------------------------------+    

Have a look at the Bash Prompt HOWTO for lots of fun details. example:

user@host:/usr/local/bin$ echo $PS1
${debian_chroot:+($debian_chroot)}\[\033[01;31m\]\u@\h\[\033[00m\]:\[\033[01;36m\]\w\[\033[00m\]\$ 

user@host:/usr/local/bin$ export PS1='${debian_chroot:+($debian_chroot)}\[\033[01;31m\]\u@\h\[\033[00m\]:\[\033[01;36m\]\W\[\033[00m\]\$ '

user@host:bin$

The PROMPT_COMMAND variable, if set, is a command that gets run before displaying the prompt specified in PS1. In your case, PROMPT_COMMAND runs an echo statement with certain ANSI escape sequences that manipulate the titlebar of an Xterm.

If you suspect your PROMPT_COMMAND is overriding your PS1 prompt, you can unset it and test things out:

$ unset PROMPT_COMMAND

Finally, be sure that you're changing the PS1 definition that actually gets used. Common locations are /etc/bash.bashrc, /etc/profile, ~/.bashrc, ~/.bash_profile, ~/.profile. The system files are generally (but not always) run before the user files.

Simple bash replace command is

${VAR/pattern_to_find/pattern_to_replace}

For showing the last directory you can just do ${PWD/*\//}, i.e. find any thing before and including the last '/' and replace it with nothing.

On my ubuntu machine I use:

export PS1='$(whoami):${PWD/*\//}#'.