As suggested in Dictionary for TeXstudio: “No dictionary Available”, I have downloaded the dictionaries that I want. I can see that TexStudio is recognizing them, from the Options --> Configure TexStudio --> Default Language, where both of my wanted languages are successfully showing. The thing is that I can decide only one of them and I cannot make them both work.
How can I make them work together (Greek and English dictionary) without switching manually every time?