Does this spell function similar to an aura, so that creatures can come and go from the 30 ft. range and be granted the bonus only while they are inside it?  Or is it a one time enhancement, where in you select creatures within the 30 ft. range when the spell is cast and those creatures have the bonus regardless of how far away from the caster they get (and creatures that weren't chosen upon casting can be granted the bonus later)?

"Pass without trace is meant to benefit you only while you're within the spell's radius"

https://www.sageadvice.eu/2016/02/19/targets-of-pass-without-trace-must-remain-within-30-ft-of-caster-in-order-to-maintain-benefit/

If an ally enters the 30 foot radius after the spell has been cast, can they be granted the buff, or do they have to be chosen at the time of casting?

I think not.

The way it reads to me is for the duration, you can choose at any point who to give the buff to.

if this was for the wizzard i would play the arcane trickster more often.

A Wood Elf Arcane Trickster can pick this up at 4th level by grabbing the Wood Elf Magic feat. This plus Longstrider can be pretty fun.

I just don't like playing elfs 

Does it stack though? Shadow Mark characters get this and i'm playing one, my party also has a ranger who is taking this. My question is do both uses stack for a plus 20 to stealth?

Nope! Multiple castings of the same spell, even by different casters,  don't stack.

The effects of the same spell cast multiple times don't combine, however. Instead, the most potent effect-such as the highest bonus-from those castings applies while their durations overlap. For example, if two clerics cast bless on the same target, that character gains the spell's benefit only once... [Player's Hand Book, p. 205]

Not available to add on spells known as Mark of Shadow Elf

my shadow monk uses this a lot it essentialy if you have a good stealth bonus this elimnates the need for a stealth check

Does this stack? Could 2 druids cast this and give the party +20?

Quote from JorDMC >>

Does this stack? Could 2 druids cast this and give the party +20?

No.  Effects with the same name don’t stack.

(But, it does stack with things like the Cloak of Elvenkind.)

Casting word is:

Departium Beyondicus

It sounds like its any creature within the circle when you cast it and remains no matter what but you can't add more after you chose the creatures in the original circle

As Chineysocks mentioned: 

Quote from chimneysocks >>

"Pass without trace is meant to benefit you only while you're within the spell's radius"

https://www.sageadvice.eu/2016/02/19/targets-of-pass-without-trace-must-remain-within-30-ft-of-caster-in-order-to-maintain-benefit/

You can make an argument that you can grant anyone who enters the area the bonus again, and I would probably allow it.

When you travel does the 30ft radius follow you

If you cast it yes I believe 

I really enjoy this because I play a earth genasi Arcane Trickster so my Plus 8 to stealth can be up to a + 18 and at higher levels I get to cast it multiple times . I am lvl 3 right now with the Capability to have a +18 to stealth it is Kind of broken and I love it