Is it possible to find same persons based on text analyzing? I needed to make a system for recognizing people based on hundreds of text by finding similarities in their written text grammatically or similarities between words they choose for writing, I don't want it so accurate but wanted to know if it is possible.

For example, finding one person with two account or more on a forum or something in that case (texts already gathered). I'm just wondering if it's possible and what field should I research in for.
The term you are looking for is stylometry, which is related to a technique in forensic linguistics called writeprint analysis. There are many different techniques to perform stylometric analysis, from the very basic 5-feature analysis classifying features such as the lexicon and idiosyncrasies unique to a person to more complex analysis utilizing neural networks and machine learning. Searching online for research papers focusing on stylometry should assist you in finding the best technique for the job.