I'm married and want to hyphenate my child's name

I have a 4 year old daughter and her father is from my previous relationship. However, I want to hyphenate my daughters last name to my newly married name. Right now, she has her dads last name only.  I don't want her to feel left out because she's the only person who doesn't have the same last name in the house hold. Is this possible? And will her father have to go to court? Please give me your feed back. Thank you 

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