Verified answer

Perhaps they mean the Chinese equivalent of your English name... you should find out to be certain. Sofia, for example, is 索菲娅 [Suǒfēiyà]. Some legal documents that identify you may require the Chinese equivalency... as is the case with a Foreign Experts Certificate, which bears your native given and family name with the Hanzi equivalent.

Since the school you are studying at accepts international students, you should realize that there are people that live outside of mainland China with legitimate Chinese names. Chinese visa applications are the same, it asks for your Chinese name... that doesn't necessarily mean you have to arbitrarily make one up because there is a blank for one... again, there are people with Chinese descent that have Chinese names that live outside of the mainland.

There are conventions in naming with Chinese as there are with English... and I'd suggest employing the help from a native speaker otherwise you could result with something quite nonsensical, foolish or derogatory. The flip-side of this is Chinese selecting English names... I've visited schools where the student's have chosen their English names; boys with girls names, girls with boys names, and kids with names like Lamp, Tide, GM, Fries, and Fly (at one school, the teacher chose names from a book of foreign brandnames).

Do you want to have a full name or you just want a first name or nickname?

A name with 小 is usually a nickname. For example, 刘雨（刘 is the family name and 雨 is the first name) will probably have a nickname as 小雨. If you want, you can make a full name in a format like "刘小雨”, which is socially acceptable.

We usually only call a person who is junior to you or a close friend "小X " as a nickname, except one has a first name contains 小.

Those three names you gave are really common names except “小一”. I mean, it is acceptable, but too simple to use it. The other two are pretty normal and popular.

Your name sofia索菲娅 is a translated Chinese name, and it has been commonly known by Chinese. I think you can use it directly as your first name. Both"小菲” “小娅” are also popular girl nicknames and I think will be better than 小雨 小星(They are neutral and too common).

I don't recommend you make up a family name. It will be weird to make up a family name not belong to you, especially if you want to use 索菲娅 as your first name, since it is in western style.

My suggestion is "小一“, it is easier to write. LOL.

It is a nice & special name and people will not forget.

Or you can take "小苏菲（XIAOSUFEI）” “小菲(XIAOFEI）” as your Chinese name.

your name is Sofia(索菲亚)， so 小菲 is quite great, I think.