If the father signed the affidavit of paternity required for his name to be listed on the birth certificate, the law considers him to be the legal father with parenting rights.  Removing his name from the birth certificate will require a legal process that involves the courts.  If you look at the website for the Department of Vital Records, you will note that both parents must sign the affidavit to change a child's name on the birth certificate. https://www.azdhs.gov/licensing/vital-records/index.php#corrections-amendments-registrants-name.  If you want to get more information, you should discuss the issue with a lawyer.  There are 3 programs in Arizona that you can use to get some inexpensive legal advice and guidance.  One is the Modest Means Program.  If you are financially qualified for the program, for a $75 fee, Modest Means offers a one hour consult with an attorney.  If you need additional help and the attorney agrees to take your case, the fee charged will not exceed $75 per hour.  The telephone number is (866)637-5341.  Both the Maricopa and Pima County Bar Associations have lawyer referral programs that offer a 30 minute consult with an experienced attorney.  Maricopa County's Lawyer Referral Service offers a 30 minute consult for a fee of $40.  The telephone number is (602) 257-4434.  Pima County's Lawyer Referral Service offers a 30 minute consultation for a fee of $35.  The telephone number is (520) 623-4625. If you do  not have sufficient money to pay for a reduced fee consult, you can go elsewhere on this website and apply to see if you qualify for a free lawyer. Go to http://www.azlawhelp.org/accesstojustice.cfm