Okay, first: welcome to the fandom! I'm gonna mostly talk about the names half of your question. There's two kinds of Erik fandom names:
- Some letter(s) appended to the front of "Erik" to denote the material each Erik is from
- A different spelling of Erik entirely, which is (sometimes) specific to the media he's from
For the first kind, there's a few notable ones:
Merik - Musical erik (the Erik in the Lloyd Webber Broadway musical)
Gerik - Gerard Butler Erik (from the 2004 Schumacher film, Gerard Butler was the actor that played the phantom)
Cherik - Charles Dance Erik (From the 1990 miniseries, Charles Dance was the actor that played the phantom)
Lerik - Leroux Erik (aka the Erik in the original 1910 book written by Gaston Leroux)*
Kerik - Susan Kay Erik (The erik in Susan Kay's novel Phantom)
Sometimes you'll see this format for specific musical actors, but that's less common and usually you can figure out what the poster means from the post tags.
*Note that I've also seen this used to refer to Lon Chaney Erik. Lon Chaney was the actor that played the phantom in the 1925 silent film. I usually see it referring to the Erik in the original novel but it's good to keep in mind.
As for the second kind there's few of these. The only one that I've seen used is Erique to describe the Erik in the 1943 movie directed by Arthur Lubin. There's also a few different Erics from various derivative works, including such spin offs as Phantom of the Mall.
These are less common overall so you're probably fine learning about them later.
And an additional note - the Destler last name came from the 1989 film directed by Dwight Little. It's been used very broadly in the fandom as Erik's last name since he doesn't have one in the original novel. Usage of the last name Destler is not necessarily indicative of the author meaning the 1989 movie Erik (at least as far as I've understood).
I fully encourage others to join in here and fill in my gaps, especially for personality - I haven't seen all the derivative works (especially the movies, that one's a big blind spot - I've seen 2004 and 1990 but that's about it lmao)