You can control the prompt in Bash (and Zsh) by setting the PS1 environment variable.
You may do this in your $HOME/.bashrc file, for example.
Example:
PS1='\u@\h:\w\$ '
or for your-user@pc use
PS1='\u@pc'
or go simple
PS1='$ '
Here's some of the magic tokens you can use.
\h : the hostname up to the first ‘.’
\H : the hostname
\u : your username
\t : time in 24hr format
\w : current working dir
You can apply colour codes too, should you wish.
EDIT: colour, bold etc.
ANSI escape sequences can be specified like \033[ then some numbers for bold and colours joined with ; then m and can be reset with \033[0m;
e.g. PS1='\033[31mxxx\033[0m ' would give you a red xxx as a prompt.
Very mini cheatsheet, replace 31 (Red) in the above with..
1;31 for bold red
1 for bold default colour
31;43 for red text (31) on yellow background (43). The second, background colour uses the same code as the foreground but +10
38;2;r;g;b where you replace r g and b with a value 0-255 for red green blue, e.g. 38;2;255;180;0 would set it to a nice orange
PS1='\033[31mxxx\033[0m ' would give you a red xxx as a prompt.
Please see an excellent answer at stackoverflow for a fuller list.