Hello.
In genuine there will be no problem while applying for government jobs if you have changed your surname after marry, there is one option for you if you don't want to change surname and continue with your original name then you can also do this and can apply for the government job easily but if you don't want to do this then you can also apply for government jobs as nowadays majority of applications done through online mode so here directly they do not accept documents for complete verification, document verification is done for those candidate who get selected for the final working, and even if you come in this final so simple thing that you will have to show is your marriage certificate or it maybe Aadhar card, with this hopefully you will be able to join with your  surname after marriage, in such there would be no problem coming after changing your surname, every time whenever you will be going for any government work so you need to show your document either it may be aadhar card or marriage certificate which can prove your conversion of surname.
Best of luck.