There are many types of fan labels out there. Some describe the dedication level put into a fandom and some may describe the enjoyment of the artist, group, or whatever. In this little rant, I'm mainly going to focus on music fans, but some of these instances can apply to fans outside of music as well.
When looking deeply into two of my favorite bands, Linkin Park and Dir en grey, and even glancing over kpop fan comments, I tend to see pretentious claims of true fanaticism. Usually people base true fan status on CD ownership, the amount of merchandise collected, artist/band knowledge, years of support or involvement, shows attended, and perhaps other various attributes. To me, I think a true fan has certain attributes of all these things, but the main point is that there is no measurement. Once numbers are incorporated with these traits, elitism is formed and new fans may be discouraged to join the fanbase or even label themselves as a "true fan". So, what do I believe makes a true fan?
You don't necessarily need to know what age Taeyang and G-Dragon were when they were trainees or that Kai was not the original drummer of the GazettE, but I believe that a true fan should at least acknowledge a band's past. Don't start an argument about Dir en grey not being a visual kei band, because they were and it will forever be part of their history despite their musical and visual transformation. Don't claim you know everything about a band when all you know is what America puts out or your knowledge is based on recent material, like the last 2 years recent. I've seen a lot of fans like this.
Financial & Emotional Support
Not everyone has a disposable income to splurge on discographies, rare items, and attending nearly every show, but everyone is capable of giving emotional support. So, you want to buy the new limited edition Alice Nine album, but you don't have the money for it right now. Don't worry, your heart is in the right place and maybe that album will still be available when you do have the funds for it. Another way to support the band is to tell other people about them. Show them where they can buy their CDs and DVDs. Imports are expensive, but as long as you're trying your best with emotional support then it's okay. Musicians are usually overjoyed when overseas fans know their lyrics, names, and costumes. This encourages them to continue forward. Even your attendance at shows and fan events is great emotional support. If you own something of theirs, that's great, but don't be all high and mighty because you own all of these obscure cassettes or vinyls and you've attended more than 30 shows.
Musicians' styles change and evolve (and sometimes devolve), this can't be helped. Not everyone is going to like these changes and that's perfectly fine. Just because you disagree with an artist/groups' direction or you dislike some songs that does not make you a bad fan. Musicians are not perfect and some experiments don't go as planned sometimes. If you look back at my post about Miyavi, I mentioned how much I love him, but I openly admitted that I wasn't particularly fond of the direction he was going with his Kabuki Boiz and even some of his current style [pre-Miyavi era]. Honestly, I think it's good to be critical of the music you love, especially when the musician sets a certain expectation with each release.
Level of Seriousness
It's okay to make fun of an artist in a positive, loving way. Musicians say and do silly things all the time. Kyo and Ruki's English isn't the best, so there have been parody videos made with fake subtitles of what the words might sound like to native English speakers to laugh at . KPop artists do silly things on variety shows and even poke fun at each other like Big Bang's Seungri imitating his bandmates. There's even performances of trot versions of popular kpop songs and parody subtitles of new kpop music videos. If artists can laugh at themselves, why can't fans? You can make fun of musicians you enjoy in a non-malicious manner. I do it all the time. Just remember there's a difference between bashing and making a joke.
All Around Respect
This might be the most important factor of being a true fan. If you claim that a musician holds a high place in your heart, then you can show them that by respecting their craft and personal wishes. Let's say that you've obtained some leaked music and you want to share it with the fandom. It's best to wait until the release date and don't outwardly expose the news to the musician. Or even better, don't share it at all! During lives, don't grope the musicians or damage their costumes or instruments. During softer songs or acapella moments, show some self control and don't yell out your love confessions or disapprovals. Have some common sense! If you see your bias offstage somewhere, don't harass or stalk them. It's fine to approach them, but there's a time and a place. They are human just like you and me and you wouldn't want some random girl peeking through your windows, harassing your family, or interrupting your dinner with a long time friend. Along with the musicians, show respect for each other. We all share one common love and that is the band/artist/group. Everyone has to start somewhere, so don't make fun of new fans who are just getting into them. As a fandom, we should support each other and together show our love and appreciation for music. Also, show respect for other fanbases even if you dislike what they like.