A lot of effort goes into fantasy names. You need to make sure they were never done before, you need to make sure that there are no double meanings, and you need to check it with other languages to make sure nothing random pops up. Occasionally this still happens, even in Magic, such as through the Kiora Atua debacle in 2014. Then again, for the first ten years, lots of cards had a bunch of Magic developers, family members, and friends all mashed up into card names.
Beginning with Alpha in 1993, vanity cards would come out every so often with these hidden names. Erhnam Djinn, for example, was an anagram of Herman, Richard Garfield's brother-in-law. Emmessi Tome? Say it out loud, and you get initials, M.S.E., which is for for former Magic designer Michael Scott Elliot. And then there is the most famous one, Wyluli Wolf, which was named for Garfield's first wife. Even hypothetical new cards, such as Barry's Land (granted that was the card's test name), got the same treatment and were named after people.
Over time these became more and more tenuous. Mijae Djinn and Ydwen Efreet were named after friend's of Magic designer Mark Rosewater who got married. Leshirac's Sigil used the middle name, "Charles", of a playtester. However, by the mid 2000s these began to be a bit too much. They were now going a bit all over the place, and the personal connections that had made them fun were now getting a bit hyper-specific.
A lot of Magic staff apparently began getting miffed about some of these names. At the same time, a lot of higher-ups were extremely worried about the special names influencing the behind the scenes decisions in the process behind making the cards. Ultimately, it was decided to stop the practice and let all future fantasy names be a bit more on the creative side.
While words from existing vanity cards are allowed, such as with Phelddagrif (most recently reprinted in Mystery Boosters) coming back in newer iterations such as Questing Phelddagrif, they're pretty much being grandfathered in. Any other tries at doing this again rend to be summarily halted.
While cards today get a bit more research, development and thought into the names, the days when a card name is directly tied to something as ridiculous as the names of people the Magic staff know are all but gone forever. Probably. You never know if vanity cards will ever come back.