How can I tell if a certain carbon/hydrogen molecule can actually exist?
When drawing organic structures Carbon should have 4 "lines" coming from/to it while Hydrogen can have only 1 covalent bond. So if you could draw your molecule following these rules, it probably can exist. Here is an example:

H       H
 \     /
  C=C=C
 /     \
H       H


Alternatively there could be this structure with the same number of "lines" coming from/to Carbon:

  H   H
   \ / 
    C     H
   / \   /
  H   C=C
     /   \
    H     H


As for the naming.. It's more complicated since it would depend on whether there is only one = bond or more than that. You could watch CrashCourse Organic Chemistry intro that talks about some naming conventions. But if you're stumbled, you could count the number of Carbons and Hydrogens and google for it: C3H4 or C3H6.