[MorganFreeman]

Why is the first compound more stable than the first?

And, are these the correct names for these compounds?

This is my first post, thanks for the help with the questions.

[macman104]

I assume you mean, why is the second compound more stable than the first?  The reason is because the C=O bond is strong than the C=C bond.

The names are the correct base names, but you are lacking numbers to indicate where the substituents are.  For example, the one on the right is 3-pentanone.  The one of the left is 2-pentene-3-ol.

[cubane]

If this were in acid then I would say equilibrium would favor pentenol, if not pentone would be favored.

[MorganFreeman]

Could it be because the oxygen is the more electronegative. Oxygen would rather form a double bond with a carbon instead of with a carbon and hydrogen because it can hold the shared electrons more tightly, right?

[macman104]

Could it be because the oxygen is the more electronegative. Oxygen would rather form a double bond with a carbon instead of with a carbon and hydrogen because it can hold the shared electrons more tightly, right?

Yes, oxygen is more electronegative so it pulls the electrons and thus "likes" the increased electron density with the double bond.