Do We Need Permission to Use this Name?
I appreciate your thoughtful impulses -- both to honor your husband's grandfather, and to honor the importance of his name to the rest of the family. Too often, we fall prey to the tempation of focusing on "rules" and whether we have the "right" to do something according to formalized etiquette. Having the rules on your side is comforting, but it doesn't change the reality of hurt feelings among the people you love. A dose of common-sense thoughtfulness is always in order.
Of course, the best rules of etiquette are based on common-sense thoughtfulness. For instance, there's a reason why the rule of thumb for grandparent namesakes is "first come, first served."
Yes, Grandpa has other grandkids, too. No, you don't have any more claim on his name than they do. But neither do they have any more claim on it than you. How do you move past that deadlock? You certainly don't want cousins and siblings jockeying for position, trying to prove they're more worthy of the name; that's a recipe for familial disaster. The thoughtful, common-sense tiebreaker is to take the path that's most certain to yield a namesake. Thus the first-born baby gets the first shot at the name.
I suggest you follow your considerate instincts, with a small tweak. Do get in touch with each of the the other grandkids and let them know you're planning to use Grandpa's name, and that you hope they feel that's a suitable way to honor him. Listen to their responses, and try to be open to creative compromises if they say they'd like to use the name in some way, too. But don't quite ask their permission. As thoughtful as that may seem, it's an invitation to open this orderly, loving namesake process to a world of trouble.