Regardless of the label applied (although, for the record, "biamorous" or "panamourous" really feel like repetitive terms).. if you're bi or pansexual, you're interested in relations with either/any gender identification.. if you're open to relations with them, you're most likely open to relationSHIPs with them. I for one can't be bothered to have sex with someone I don't care at least a little about, so I don't see the difference between, for example, "bisexual" and "biamorous".. if I want to sleep with you, I probably like you, and possibly could love you.. if I like you, it's entirely possible that I might want to sleep with you, and if I love you, that possibility goes up exponentially.
THAT BEING SAID.. I would absolutely invite you to identify however you are most comfortable.. the value of "labels" is their ability to transmit larger amounts of information in a smaller, more concise way. Therefore, we choose and invent labels to avoid longer explanations and try to reduce confusion. I'm not big on them.. but I am always interested in hearing them, in an attempt to understand that person.
Being married to a self-proclaimed pansexual polyamorous lesbian who's chosen to marry hetero... (yes, it makes sense.. she chose me specifically, as a human, not as a gender.. she still believes that if it were not for me she'd be dating/in relationships with women only, and just occasionally enjoying the company of a man, but not in relationships with them.. and she'd still desire other female lovers too.. wow.. see? complex).
This has the benefit of helping one understand the value of short forms. Hearing her explain to someone her life theories is sometimes unbelievably complicated.. as you can see.
I think the only real drawback is when people mistake the label as "the last word" or misunderstand them.. or even deliberately misrepresent them. (Like when people say bisexuals are just confused.. bull) It's a hint about someone, a starting point.. eventually, humans can only be understood by taking their complexity into account.
Apply or wear labels as you wish.. do so justly and without malice.. they do have some value.. even if they're only a starting point to a greater understanding.