I have just installed Ubuntu 16.04 on an old phone (Nexus 5).
It seems to work but it doesn't look like the same version of Ubuntu I have on my laptop. Navbar is at bottom, name of console is 'LXTerminal'.. so I am a bit lost.
Is there a way to recover usual Ubuntu 16.04 appearance ?
Unless your phone can handle it, and the option is available in Linux Deploy (last I remember it wasn't, the Unity DE), then no. Otherwise, try reinstalling the distro with the Unity DE.