I installed Synaptic too and it shows up as Synaptic Package Manager in Slingshot (under System Tools if you use category view). By default it uses quite an ugly icon, this is how it looks like for me (with an extended icon pack and unstable WingPanel):
One idea would be to check the
synaptic.desktop file in
/usr/share/applications/. It should look something like this:
Name=Synaptic Package Manager
Comment=Install, remove and upgrade software packages
Quite important are the entries
NotShowIn (should not contain
OnlyShowIn (if it's there, make sure it does contain
Pantheon). There should not be an entry called
NoDisplay. (Learn more about recognized desktop entry keys.)
If there is no such file first try to reinstall synaptic
sudo apt-get install --reinstall synaptic.
If that does not work, use Scratch to create a new file called
~/.local/share/applications/ with the contents I have posted above.