Modification of Custody: Would This Be Reason for Change of Last Name

My question involves a child custody case from the State of: VA

My daughter has her father's last name. I was okay with it when she was born because I was under the impression that we would get married. Didn't happen. He has not seen or talked to her since last July. I have even reached out to him two or three times and he did not respond to my emails. He did respond to a bill I requested him to pay (he wasnt too happy about it)

We currently have shared custody and he has visitation every other weekend (on paper) I am taking him back to court to change our custody arrangements and to either request sole custody or shared custody with me having the final say.

I would like my daughters last name to be changed mostly because it would make everything much easier for me. Another reason is that if someone just sees her name they assume it is also my last name. My daughter is 5.

What I read online is that name changes are not so easy and not without a legit reason. Is it reason enough for me to just make it easier and for my daughter to have my last name?

thank you,

Modification of Custody: Would This Be Reason for Change of Last Name