Two kids with different last names from the same two parents?

One of the top names we are considering for our baby girl is also the first name of my hubby’s cousin. We don’t know her well but his close relatives do, so we thought it might be weird if our baby has the same first AND last name as her (since the cousin has the same last name as my husband). We would consider giving our child my last name instead, but my biggest hangup is that we already have a daughter with my husbands last name.

So... which is weirder: naming our child the same first and last name as his cousin, or giving our two kids two different last names?

Or maybe we have to start from scratch... but time is running out!