Pip for Python 3
The Python 3 version of pip is pip3 so you would run:
pip3 install <package-name>
In general, you can run dpkg with the -L, --list option to see what files are in an installed package:
dpkg -L python3-pip
I just installed python3-pip to verify this and one of the files listed is /usr/bin/pip3.
The two versions of Python can quite happily co-exist with each other.
System Python 2
I wouldn’t advise uninstalling the Python 2 that came with Ubuntu as it’s required by useful tools and important OS utilities. There’s a Debian project to port its Python 2 OS code to Python 3 but they won’t be finished for some time.
As an experiment, I tried running sudo apt-get remove python and I was asked to confirm if I wanted to uninstall a long list of packages:
apturl blueman flashplugin-installer gconf2 gdebi gecko-mediaplayer gimp gir1.2-ibus-1.0 gksu gnome-mplayer gvfs-backends ibus inkscape iotop ipython libgda-5.0-4 libgda-5.0-common libgksu2-0
libgnomevfs2-0 libgnomevfs2-common libgnomevfs2-extra libsmbclient light-locker-settings lubuntu-desktop lubuntu-software-center mplayer2 ndiff offlineimap pidgin python python-apt python-aptdaemon
python-aptdaemon.gtk3widgets python-bs4 python-cairo python-chardet python-colorama python-crypto python-dateutil python-dbus python-debian python-decorator python-defer python-dev python-distlib
python-gi python-gi-cairo python-glade2 python-gobject python-gobject-2 python-gtk2 python-gudev python-html5lib python-imaging python-ldb python-lxml python-matplotlib python-mock
python-ndg-httpsclient python-nose python-notify python-ntdb python-numpy python-openssl python-pexpect python-pil python-pip python-pkg-resources python-psutil python-pyasn1 python-pyparsing
python-pysqlite2 python-requests python-samba python-scipy python-setuptools python-simplegeneric python-six python-sqlite python-talloc python-tdb python-tk python-tz python-urllib3 python-wheel
python-xdg python3-smbc samba-common-bin samba-libs smbclient system-config-printer-common system-config-printer-gnome transmission-gtk ubuntu-release-upgrader-gtk update-manager update-notifier
update-notifier-common vlc-plugin-samba
Needless to say, I didn’t confirm.