Do I need second master's degree or not?
There is usually not a formal requirement for PhD candidates to have a master's degree in the subject of their PhD. Indeed, having a master's degree from a field different to that of the PhD is very common in some disciplines.

The main thing to bear in mind is that applicants for a PhD programme must convince the admissions committee that they have the skills and academic potential that will be necessary to successfully complete the programme. When completing your PhD application, think about the kinds of skills and background knowledge that will be important for your PhD and explain why you have those skills, or why the admissions committee should believe that you are able to quickly acquire them