During her first year as a member of the team in Young Justice, M'gann M'orzz, aka Miss Martian, took on the name "Megan Morse" when she went out in her human form. It was primarily used to blend in at high school, pretending to be a normal human as opposed to the superhero from Mars she really was. At first glance, it might have seemed simply like she had chosen a name that matched her one on Mars, but as the show went on, the tragic reason behind the name became clear.
Having become obsessed with Earth TV during her time on Mars, M'gann started emulating the mannerisms and behaviors of the main character in her favorite program, Hello Megan. She even used the catchphrase from the show, "Hello Megan," as her own during the events of Season 1. The show was fairly old and was something the rest of the team had never heard of -- well, at least until Season 1's "Image," which sheds some light on M'gann's behavior.
During a mission to stop Queen Bee from taking over Qurac, the group comes across the lead actress from Hello Megan, Marie Logan, who M'gann is unsurprisingly ecstatic to meet. However, Marie was rather dismissive of the work she had done all those years ago, regarding her work in the show as something she regrets -- a revelation that understandably affects M'gann, given how closely she had tied her identity to that of the show.
During the episode, the other members of the team also learn about the show and how M'gann was using some elements from the series in her life, including taking the name of one of the characters, Connor, and suggesting it for Superboy. Understandably, the other heroes are a bit weirded out by the whole situation, but are much more accepting when M'gann explained her reasons for it.
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As it turns out, M'gann is a White Martian, something she'd hidden from the rest of the Team for fear of losing her friends. On Mars, White Martians were a discriminated minority, and M'gann had to bear the brunt of that during her early years, which is why she found comfort in Hello Megan. For her, it was a method of escapism from her hardships, and even when she finally managed to leave the planet and join her uncle J'onn J'onzz on Earth as a superhero, it was still something she enjoyed.
Queen Bee found out about this and exploited it in an attempt to blackmail M'gann into doing her bidding. Fortunately, M'gann was able to overcome on her own and with the help and encouragement of her friends later on. As she learns by the end of the episode, her time on Earth that as a superhero managed to carve out her own identity and allowed her to grow even as a person. While Queen Bee thought M'gann's true form was her weakness, it actually turned out to be her strength.