I think middle-earth roleplaying did a really good job with that!
They went with: allright what were they to start with? One a servant of Orome, the other of Mandos and extrapolated from that..
So Alatar became a far striding nomad, a horseman, an archer and hunter, the more adventuring and daring, but also more warlike and agressive one of the two.
Pallando became a darker charakter, a doom-sayer, a prophet, a cultist and founder of religious sects, someone connected with death-worship and spirits.
I can relate to that and understand why and how they constructed this from the few things we know.
Could we get to other conclusions? Alatar might mean radiance-lord or protector, Pallando perhaps "far one" or "distant one". Morinehtar, darkness-battler and Romestamo easthelper, or maybe east-maker or east-smith?
One could extrapolate from that perhaps stories of a very charismatic character, one associated with light and brightness who acts as a great defender and a reclusive or very distant character, one who acts hidden, maybe through agents or messengers and who himself stays behind the scenes and is hard to catch.
Or one character who clearly is a great warrior and effective fighter, maybe even a warlord and destroyer of evil and another character who is very benevolent, or a great maker and forger of cultures and peoples.
I always asked myself if there are mythological figures or historical figures which might resemble them...
And i came to think of characters like the great chinese immortal old wiseman of the mountains, or perhaps even the great yellow emperor himself, or historical figures like Laotse or Kunfucius. And perhaps the great ancient arabic wiseman and magician, the starseer, or historic or quasi-historic figures like Zarathustra, Moses, Abraham, or the old man of the mountain and with his assassins or Siddhartha Gautama.
At last i think one should be connected with the unknown far east of Middle-earth, the other one with the unknown lands of Harad.
Just ideas...