Ok so you need to apply for a child arrangement order for contact and a specific issue order for the name change.
A ‘specific issue order’ is used to look at a specific question about how the child is being brought up in this case to prevent the change of name. Follow these steps to apply for a court order:
1) Read guidance CB001 on making an application: https://www.gov.uk/government/publications/family-court-applications-that-involve-children-cb1
2) Fill in the C100 court form found here: https://www.gov.uk/government/publications/form-c100-application-under-the-children-act-1989-for-a-child-arrangements-prohibited-steps-specific-issue-section-8-order-or-to-vary-or-discharge
3) Send the original form and 3 copies of it to the nearest court that deals with cases involving children, you can find the nearest court here: https://courttribunalfinder.service.gov.uk/search/
It costs £215 to apply for a court order. You may be able to get help with court fees if you’re on benefits or a low income and you can find out more here: https://www.gov.uk/get-help-with-court-fees
I would advise you to seek a child arrangement court order such an order can set out who looks after the child and when. Such an order once made can be enforced if it is breached. In order to do this, you will need to arrange for and attend a mediation appointment with your ex first to see if an order can be agreed. Even if you and your ex end up having to go to court to sort out the differences, you will normally need to prove that you’ve been to a mediation information and assessment meeting (MIAM). This is an introductory meeting to explain what mediation is and how it might help you. If your ex doesn't want to see a mediator, you should go to the MIAM on your own. You’ll then be able to prove you’ve tried mediation if you later want to go court. You can’t force your ex to go to mediation. In order to find a mediator you can use this link on the Family Mediation Council website here: https://www.familymediationcouncil.org.uk/find-local-mediator/
You’ll normally have to pay about £30 for an MIAM, although sometimes this first meeting is free. Follow-up sessions usually cost you and your ex about £80 each - most people need to go to 3 or 4.
The cost of mediation varies depending on where you live. Phone around to find the best price, but bear in mind the cheapest might not be the best.
If the MIAM does not work and you not able to agree to mediation you will need to go to court. This will require you to fill out form C100 which can be found here: https://www.gov.uk/government/publications/form-c100-application-under-the-children-act-1989-for-a-child-arrangements-prohibited-steps-specific-issue-section-8-order-or-to-vary-or-discharge
You can find guidance on filling out the application here: https://www.gov.uk/government/publications/family-court-applications-that-involve-children-cb1
Send the original form and 3 copies of it to the nearest court that deals with children, you can find your nearest court here: https://www.gov.uk/looking-after-children-divorce/apply-for-court-order
The application will cost £215. If you want to find a solicitor to assist with this process and represent you at the hearing you can find a solicitor using the Law Society find a solicitor search option here: https://solicitors.lawsociety.org.uk. You can search by town or postcode to find one near you, as well as area of law in this case family law.
I trust this assists