How do I change the format of the name in Terminal? I don't know what this is called, can anyone clarify? Is it called the name / hostname. I don't know what you call it.

On Ubuntu my Terminal shows kalima@coolbox:~$

But on OSX my Terminal shows compname:~ kalima$

Is this normal? Is there a way to change it so they're both consistent in format?
That's called your "prompt". You can define the PS1 variable to control it.

Add the following to your ~/.bashrc file:

PS1='\u@\h:\w\$ '


See the bash manual for more details.