What is the ruling on a girl calling herself by names such as "The Protected Pearl," "The Hidden Jewel," "A Queen by My Commitment," or "A Queen by My Niqab" in forums and websites? And is this considered self-praise?

The Shari'ah prohibited naming with names that involve self-praise, as it is narrated in Sahih Muslim that the Prophet, peace and blessings be upon him, named Barrah as Zaynab, and said: "Do not praise yourselves; Allah knows best who among you are the righteous." Every name that involves aggrandizement or glorification is disliked. As for the titles mentioned in the question, they do not fall under the prohibited self-praise.