Finding molecules that you randomly create using a modeling kit
Here's a list of all the stuff you can try:

For you, the common theme of all these steps would be to be able to correctly identify the skeleton of the molecule that you built yourself, and then being able to draw it on the online molecular editor.


Sign into Reaxys or SciFinder, draw your structure, and search for molecules or reactions. Note that these require institutional access (or a very hefty fee).
ChemSpider Structure search: It's a free tool, and my personal goto for getting access to several matching compounds. You can search for "exact matches", or partial matches like "tautomers", "same skeleton", or even "all isomers". There's search filters as well. But again, the first few options are sufficient for your snatoms kit.
eMolecules (in case you didn't notice, we also advertise it in our right sidebar) very similar to ChemSpider above.
PubChem Structure search - again, similar to the above two. Note that though this one has an odd (and old-looking UI) which you might not find intuitive.


The main difference between all four of these is primarily the level of detail and depth of their data. Functionally, they all do the same thing. But, they do so on different databases. That means for more complex molecules, their outputs may differ. However, this hopefully won't be a problem with your simple snatoms kit, so you can go ahead and try any of them. Good luck!



Addendum: generating a 3D structure from the molecule name

You may use this free online tool based on JSMol. Type the IUPAC name of the molecule (say (1-methylcyclobutyl)benzene) into the lower right box, and press Enter. Its 3D structure is then immediately transferred into the box above. You can zoom it in or out, or rotate it by 360deg. This would help when you're trying to create the 3D molecular structure given the IUPAC name.