What is the correct term to describe matter converting into energy? Matter and energy are related; one can convert into the other. What is it called when this happens?
For example, solids melt/liquefy into liquid, and liquid vaporizes into gas. Gas condenses into liquid, and liquid solidifies into solid.
So matter [verb] into energy, and energy [verb] into matter. What are the correct verbs to use here? I am thinking that they are "energize" and "materialize", but I'm not sure, especially about "energize".
 A: Annihilation is the word you must be looking for. When a low-energy electron annihilates a low-energy positron (antielectron), two or more $\gamma$-ray photons are produced, the process is called annihilation$_1$. If a $\gamma$-ray photon materializes into an electron and positron pair, the process is called pair-production.$_2$  
Probably you must have got one verb "materialize" but you haven't got the verb for vice versa process.   

Credits: $_1$Wikipedia-Annihilation $_2$Modern's ABC of Physics-XII-2013 Edition-Page NO.7.Original data is subjected to modification. 
A: Energy is conserved; energy is neither created or destroyed, but, rather, converted from one form to another.
Matter (invariant mass) is, on the modern view, simply one of many forms of energy.
Matter isn't converted into energy; matter can be converted to another form of energy and, another form of energy can be converted into matter.
A: It is not conversion rather an equivalence. If a closed box at rest contains an amount of energy of E then the mass (defined as the inertia of the box) will be E/c^2. It doesn't matter if that energy is simply a solid ball of iron or if it is thermal radiation. 
A: There is some confusion here:

Matter and energy are related; one can convert into the other. What is it called when this happens?

Matter in the sense of "mass" is related to energy through the famous E=m*c**2 of Special Relativity. That is the only framework where conversion of matter to energy has a meaning in physics. 
Your example:

For example, solids melt/liquefy into liquid, and liquid vaporizes into gas. Gas condenses into liquid, and liquid solidifies into solid.

is out of classical  physics, thermodynamics, and it is talking of phase transitions of matter. There is no change of matter to  energy or energy to matter in your example. There is only a change in the form of energy, from kinetic to potential, binding the individual atoms and molecules dependent on the temperature . So solids turn into liquids and liquids to gas depending on temperature. "turn" is a better turn of language :) to "transition" which is the physics term. 
Then again you go into a phrasing that is appropriate for special relativity:

So matter [verb] into energy, and energy [verb] into matter.

Here you can use "converts" if you are discussing fusion and fission reactions, mass converts to energy, also "becomes" and "turns" are not wrong turns of phrase. If an energetic photon creates an electron positron  pair in the field of an atom or nucleus, "the energy of the photon partially  converts to matter" is fine ( a lot of the incoming energy goes to kinetic energy, momentum balances, and a scattered photon of less energy). 

What are the correct verbs to use here? I am thinking that they are "energize" and "materialize", but I'm not sure, especially about "energize".

"energize" is wrong, "materialize"  is too science fiction.
