Family baby name

Anna
We want to name our daughter after my mother who was named after her grandma. So the name is in the family twice and i just found out it is my husband's great grandma's name also. My sister thinks it is odd to give her the same name as my mother. My mother will be taking care of her during the day. Is that too awkward? It's a short name so no real options for nicknames. My mom, mother in law and i all have the same middle name so i was going to use that. This is causing so much stress!