Fresh passport application and name change (Male)

I dont have a passport as on date, but had applied a few years ago when in college. I had attended the interview back then and because i did not have my birth certificate, They had asked me to come back with a govt. issued copy. I got busy with my job later and never went in to get the passport done. I got a letter four months ago that my file has been closed and i have to quote the old file number if and when i apply for a new one. Now, I want to legally change my name to "Siva Rudra" for numerological reasons. My name as on my DL/Voters ID/Aadhar Card/10th Markscard is "Sivanathan Rudra K A" My name as on my PAN Card now is "Sivanathan Rudra Kashi Natarajesha Ayyappan" My fathers name is Kashi Natarajesha Ayyappan. I am aware of the process to change the name, but my question here is, Would it be better if i change the name legally first and then apply for a passport or first apply for a passport on the old name and then change the name on the passport post issuance?