They are more of personal choice or sometimes jokes:
For George R.R. Martin
Martin has chosen a turtle as his personal sigil, and he is often seen
wearing a hat with a turtle pin on it. As Martin himself explained at
the Game of Thrones panel for San Diego Comic Con 2012:
"Turtles have always been my sigil, I suppose. When I was a kid,
growing up in Bayonne, NJ, I lived in a federal housing project, and
we were not allowed to have a dog or cats. The only pets I could have
were turtles. So, I had an entire toy castle filled with dime-store
turtles. I gave them all names, and since they were living in a toy
castle, I decided they were all knights and kings...and I made up
stories about how they killed each other and betrayed each other and
fought for the kingdom. So, Game of Thrones, actually began with
turtles. I decided later to recast it with actual human beings."
For Bryan Cogman
The sigil next to Cogman's name in the opening credits is actually a vomiting maester - a joke by Benioff and Weiss, referencing how at the Season 1 wrap party, Cogman had too much to drink and had to throw up
He even mentioned it himself in a tweet (now deleted):
Most of us producers got to choose our personal sigils for the opening credits. Except me. D&D personally commissioned the vomiting maester
— Bryan Cogman (@b_cogman) April 8, 2016
Ramin Djawadi, Gemma Jackson, Guymon Casady and Deborah Riley have turtle as their sigil too.
Carolyn Strauss has an Ostrich
The symbol of Ostrich has a famous relation with the surname Strauss:
The name has been used by families in the Germanic area for at least a thousand years. The overlord of Gröna, for example, went by the name of Struz and used the image of an ostrich as his symbol. Examples of it could still be seen on the thousand-year-old church bell of that town. "Struz" or "Strutz" is the North-German form of the word "Strauss", which is the modern German word for ostrich.
Took images and some inspiration from the answer on a similar question from our sister sci-fi site, which also provides additional sigils for rest of the crew too:
Where are the cast and crew logos in Game of Thrones opening credits from?