Hmmm. Interesting question. I thought this was going to be along the lines of "Would you pick matchy names, names that start with same letter", etc. I've never before even thought about it in terms of which name I liked more or which name would fit, etc.
Well, now that I think about it, if it were boy/girl twins, obviously you pick a boy name and a girl name, just like back in the days when nobody knew which gender baby they were having.
For same sex twins, (and the majority of fraternal twins are same sex) I would probably decide to name the first born twin the name I liked more. This happens in families in which there are no twins, after all. For instance, my sister gave her second son the name that was second choice to the name she gave her first son. It makes sense that this would happen fairly frequently.
My brother and his wife have fraternal twin boys. They had always wanted to name a son
John Richard Jr. So they named the twin that was born first
John Richard Jr. and the one that was born second
Andrew Bryan,
Andrew simply because they liked the name, and
Bryan was the name of the twins' older half-brother through their mother, so he'd have a tie with his half-brother, whose last name was different. My husband always wanted a
William James IV, so if we'd had twin boys, it would have been the same with us---the one born first would have been
William James IV and the one born second would have a different name, the first chosen because we liked it and the middle would have been honoring some other family member.
My niece has fraternal twin girls named
Charlotte and
Aubrie. This would be an interesting question to ask her, how she decided which would have which name.