As I know, maiden name and patronimic name are different things. Maiden name - is a surname women had before get married, patronimic name - is your father's name, like, my name is Agatha, my father is Sergey plus my surname - S., so my patronimic name would be Sergeevna and all name = Agatha Sergeevna S. Middle name - is a second, or third, or fourth name (especially in catholic religion) like Lucia Josephina Vanga.
Am I right? And what meaning do these names have in this site?
I didn't find patronimic name in profil. May be it exists but i don't know where I should look for?

I never knew what a patronym was until after wikipedia and your post. I now have a better idea. I also understand the problems Itsourtree has with the international nature of its web site. There is not a field for patronimic names.

I am not sure it this helps: The way the search works with Itsourtree is by looking for groups of letters, even within words. Therefore, combination of names can be found. This allows you to put whatever you want in the maiden name, last name, or display name. You can put as much as you want, depending on the amount of space designed (I think it is about 40 characters). The only caveat is the sequence of words. For example, if you have the name xxx yyy zzz and search for xxx zzz, the search cannot find the person.

Lastly, with backing up your files to GEDCOM, the program exports the names very well so most of your work is saved. It does not save the display name however. I have to copy the display name into the biography section to make sure I have an archive. There are some errors and bugs in the export however, and not every genealogy program will read every field in Itsourtree’s GEDCOM. However, at least it is stored offline.

Because of these facts, I have arranged and rearranged and again re-rearranged the data on my site to allow for search-ability and archive-ability. You can use this information for storing and displaying patronymic names.

Hope this helps.