It Is Known
George R. R. Martin
The answer by @RicoRicochet gives the reasoning for his in that it is a turtle because "Turtles have always been my sigil, I suppose.".

Bryan Cogman
This is allegedly a vomiting maester after Bryan had a bit too much too drink at a wrap party though I'm not sure how true the claim is.
Look closely next to writer Bryan Cogman’s name in the opening credits and you’ll see his ‘House Sigil’ is a vomiting maester. This joke was made by Benioff and Weiss in reference to a wrap party at which he er, overindulged himself, back when he worked as their assistant.
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Ramin Djawadi
George's turtle.

Gemma Jackson
George's turtle.

Guymon Casady
George's turtle.

Deborah Riley
George's turtle.

Carolyn Strauss
An ostrich is Strauss in German.

It Is Not Known
I've seen it noted that the crew got to choose their own sigils for the credits but I haven't actually been able to track down a reliable source for the claim yet though it sounds plausible.
Nina Gold, Robert Sterne
Fleur-de-lis not sure why.

Michele Clapton
Some sort of bird posturing.

Frances Parker A.C.E
I can't really make it out but some sort of cat or a helm looking left.

Kramer Morgenthau A.S.C
What looks to be a hammer.

Vince Gerardis
Some sort of flower.

Alan Taylor
The same as Kramer.

Vanessa Taylor
Appears to be a bird or fish.

Bernadette Caulfield
Triangular symbol, hut?

Frank Doelger
Four stars in a cross.

David Benioff, D.B. Weiss
Appropriately two skulls.

Joe Bauer
A crab.

Steve Kullback
A man holding up the moon?

Crispin Green
Two crossed swords.

Gregory Middleton A.S.C C.S.C
The same as Frances Parker A.C.E.

Lisa McAtackney, Greg Spence
Lisa's is a quill and Greg's is a flying bird.

Chris Newman
Some circular pattern.
