the Madurai Bench of the Madras High Court has held that single mothers need not disclose the name of the child's father at the time of registering the child's birth.

2) 

a single mother applies for a birth certificate for a child who is born from her womb, the authorities can ask her to furnish an affidavit and then, issue a certificate, unless there is a court direction to the contrary.

2. The confidentiality of the donor (in this case, the child was born with the help of a semen donor) requires to be protected. This is important for single mothers who choose to conceive through an intrauterine fertility treatment.

3. It is the State’s responsibility to ensure that no citizen suffers any inconvenience or disadvantage merely because the parents fail or neglect to register the birth.

4. As the concerned child has been born through an intrauterine fertility treatment and from the woman’s womb, it follows that the authorities cannot insist on disclosure of the father’s name.

You cannot write your name against the column meant for father's name. 

You can mention your name alone as single parent,  which is permissible in law. 

Ministry of home affairs issued a circular to all chief registrars of birth and deaths that to ensure that no one is denied birth registration of a child of a single parent / unwed mother

as per the judgement held by Supreme Court of India in ABC Versus The State (NCT of Delhi) that When a single woman or unwed mother applies for her child's birth certificate, it must be issued on the basis of her affidavit and without insisting that she disclose the name of the father. The view of the court is that paternity is inherently nebulous especially where the child is not an offspring of marriage.

if a single parent/unwed mother apply for the issuance of a Birth Certificate for a Child born from her womb, the Authorities concerned may only require her to furnish an affidavit to this effect, and must thereupon issue the Birth Certificate, unless there is a Court direction to the contrary”. The court also directed that no citizen suffers any inconvenience or disadvantage merely because the parents fail or neglect to register the birth.

1. A child born through IVF is treated as the biological child for all legal and practical reasons.

2. If you have raised the child as a single parent then you can have your name entered in all the documents of child as a single parent. I have done a similar case where the mother who had raised child as a single parent was not allowed to enter her name alone in the passport of child, but the High Court ordered the authorities to issue the passport of child with only mother's name.

3. If authorities disallow you to enter your name alone in child's documents then you should file a writ petition before the High Court.

1. Ordinarily husband's consent is required for the wife to go for IVF process.

2. I am aware of an unmarried lady whose application for getting impregnated   through IVF method has been refused by the concerned Hospital as the law is not clear about it.

3. Since you are a divorcee, you can fill up the form leaving the father's name blank. 

4. it is further clarified that the law is not clear about the cases where the single lady wants to get impregnated through donor's sperm.

You cannot write your name as father name 

2) you can furnish affidavit that child is born through IVF and not aware of father name 

1. What will you do if the school authorities object to writing your name in the father's name column also. 

Would you then agitate over it?

Instead you may better leave it blank and explain that the child do not have father and the sperm donor cannot be a father to the IVF  child. 

Later on you can decide to follow legal route if your decision to establish your rights are deprived. 

2. You can decide about it based on the prevailing circumstances. 

1. As I have informed in my earlier post, the law is nor clear on the instant issue.

2. In Kerala one unmarried  lady had to approach the Apex Court for getting her son admitted in school without mentioning her son's father's name.

3. It appears that you shall have to approach the Court for getting rid of this problem and yours will be a landmark judgement in the instant issue.

1. Keep it blank.

2. If govt or its instrumentalities do not accede to your demands then only recourse is before the courts.

3. Even if you write "NOT APPLICABLE" they will still reject it, which will be redeemable only through legal remedies before courts.