Will there be any issues in my application or in the job itself
No, unless you end up in a [crazy company][1] changing your name like this is perfectly normal. You're not even changing your last name entirely but merely expanding it to a double name, which is something that married women already do routinely.
In the US there is no need for your legally registered name to match the name you commonly go by, whether that's a first or last name. Name change laws vary by state but in general your assumed name can sometimes be considered a legally assumed name even without following the necessary paperwork for an "official" name change. Note that a pseudonym that has no relation to your family generally doesn't have this benefit.
All hiring paperwork should probably list your official name associated with your SSN to avoid payroll or benefits issues. You should also make sure that your resume and online profiles make a reference to your previous name. You'll want to make sure that you make it exceedingly clear in the hiring process that you're currently going by your new name, to avoid email accounts or other things being created based on your official name.
For further reading and things to consider before going through with your name change you should have a look at these questions:
- How do I handle my last name changing after marriage?How do I handle my last name changing after marriage?
- Risks in future career opportunities because of a legal name changeRisks in future career opportunities because of a legal name change [1]: http://www.askamanager.org/2015/09/my-new-company-wants-me-to-change-my-name.html