Changing a Child's Name: Changing Last Name of My Children

My question involves name change laws in the State of: Connecticut.

I have been divorced for 7 years now. For the past 4 years that has been no contact, visitation and minimal efforts at child support for my two minor children aged 11 and 9. Both children have, on various occasions requested to have their last name changed to mine. I am not remarried however my boyfriend and I do have a child together who has his last name. My children wish to have their last name changed to mine and perhaps eventually be adopted by my boyfriend when we get married ( Not sure if this is something we are going to embark on )

Support Enforcement as well as I, do not have a valid address on file for him. His last known phone number that I have is answered by a woman who says I have the wrong number and his last known address, his family members, states he moved out 4 years ago.

Can I petition to probate for a legal name change based on these reasons?

I appreciate any advice or insight. Thank you.

Changing a Child's Name: Changing Last Name of My Children