Learn French: L'espion garde son alias en dépit de la surveillance. - The spy keeps his alias in spite of the surveillance.

In terms of meaning, they are identical; both mean "despite" or "in spite of". However, en dépit de is slightly more formal and literary than malgré. Notice that both of these prepositions must be followed by a noun phrase (like la surveillance), never a conjugated verb.

Would the de in en dépit de change if the noun wasn't feminine singular like la surveillance?

Yes, it follows the standard rules for contracting de with definite articles. Because surveillance is feminine, we use de la. If it were a masculine noun like le danger, it would contract to en dépit du danger. For a plural noun, it becomes des (for example, en dépit des risques).

Could I follow en dépit de with a verb instead of a noun, to say "in spite of being watched"?

No, en dépit de can only be followed by a noun or a pronoun. If you want to use a conjugated verb to express the same idea, you need to switch to a conjunction like bien que (even though) followed by a verb in the subjunctive mood, for example: bien qu'il soit surveillé.

Is the final "s" in alias pronounced?