Reaction of copper (II) ion reacting with sodium hydroxide
Yes, the reaction is correct however it may be preferable to either include all or no spectator ions.
Use either a net ionic equations (omit the Na+), molecular equation (include the copper compound full) or complete ionic equation.

For example, if the compound is copper sulphate the equations would be (without states)

Net ionic
$$\ce{Cu^2+}+\ce{2OH^--&gt;Cu(OH)_2}$$
Molecular equation
$$\ce{CuSO_4}+\ce{2NaOH-&gt;Cu(OH)_2}+\ce{Na_2SO_4}$$
Complete Ionic Equation
$$\ce{Cu^2+ +SO_4^{2-}}+\ce{2Na^+ +2OH^--&gt;Cu(OH)_2}+\ce{2Na^+ +SO_4^2-}$$

Edit

In the case where you don't know what copper compound it is, use a net ionic equation. As a side note, copper hydroxide is not white. You might want to check your calculations.

If you're wondering what it is, check what other compounds will emit green.