Want to maintain father en name after marriage.

A married women normally retains the right to use her maiden Name and she is not required t adopt the Name of her husband. This may be important to a woman who has developed a long standing professional use of her Maiden name. Thus, a married woman  may adapt her husband's surname as a matter of custom rathern than as a matter of law.

Historically, a person was free to adopt and use any Name he or she desired as long as it was not done for fraud and did not interfere with the rights of others. The persons would be legally bound by any contract or other agreement into which he or she entered under the adopted Name. Also, the person could normally sue and be sued in the adopted Name.

The signature is a mark used to represent by Name and intended to operate as his signature. The signature does not have to be a full expression of a person's legal Name, but can include abbreviations, initials, nick-names, or any other mark intended by a person as his signature. 

I have answered in your similar query.

Your understanding is incorrect. Changing surname by girls after marriage is not at all difficult or hazardous.

But, if you wish to retain your original name, there is nothing wrong with that too. Please refer to my answer to your similar post too.