I would use the same name.
My cousin and i lived close and were due 3 months apart with #1.

We were the only family each other had as we lived in the sticks

Anyhow we were talking names one day and i said if i has a boy i would call him james, She said omg i was the thinking the same thing. We thought it was cool - i mean they will be 2nd cousins (and how many of your 2nd cousins do you see a lot anyhow) and they would prob think it is cool to know someone with the same name.

so neither of us cared.
She has a boy called him James and i had a girl.

but even if it was a boy they would both have the same name,

i find the whole name battle with family and friends a little silly to be honest.

It is your life - you choose what you like. i am sure your babies will meet 100 x people in their life stime with their name - esp if it is a common one.