Trademark

Shall not be registered : Provided that a trade mark shall not be refused registration if before the date of application for registration it has acquired a distinctive character as a result of the use made of it or is a well-known trade mark. (2) A mark shall not be registered as a trade mark if ---- (a) it is of such nature as to deceive the public or cause confusion: (b) it contains or comprises of any matter likely to hurt the religious susceptibilities of any class or section of the citizens of India; (c) it comprises or contains scandalous or obscene matter; (d) its use is prohibited under the Emblems and Names (Prevention of Improper Use) Act, 1950. (3) A mark shall not be registered as a trade mark if it consists exclusively of- (a) the shape of goods which results from the nature of the goods themselves; or (b) the shape of goods which is necessary to obtain a technical result; or (c) the shape which gives substantial value to the goods. Explanation --- For the purpose of this section, the nature of goods or services in relation to which the trade mark is used or proposed to be used shall not be a ground for refusal of registration.

For this type of issue happen many times. so many of law firm company uses trademark management software

You can do your Trademark Registration with different logos. As the matter of fact 1 class 1 logo, Further given that the logo should represent the wordmark of the Trademark Application. And if you want to register different logo then you can register logo in different trademark classes. 

Furthermore, If you don't want the same name under the logo then you need to file a Fresh application to get the logo Trademarked. 

To File Trademark Application click.