There was two different researches which I have planned to conduct with some participant guys who have psychological difficulty in recalling people,s names in order to figure out how they are suffered from this. soa natural?

There were two different studies I planned to conduct with participants who have psychological difficulty recalling people's names. The purpose is to figure out why they are suffering from this.

"Was" is used when talking about a single thing. (There was a study.)

"Were" is used when talking about more than one thing.

A "study" is planned research on a subject. You can do research on something, but you wouldn't do "a research".

"Some participant guys" isn't how it would be worded. It could be "some participants" or "some male participants" or "participants". The word "guys" is very informal and wouldn't be used in a scholarly paper (which is what this sounds like).

I broke it into two sentences because it felt too long and would read better as two.

"How they suffered" implies that you are trying to figure out what they are experiencing with this problem.

"Why they suffered" implies that you are trying to figure out what is causing it. I assumed that is what you meant.

I hope this helps.