My first record

It's my first record in my notebook.
My name is Katya. My full name is Ekaterina and I'm 21 years old. I have lived in Moscow a long time.
I love traveling and so I want to learn English. I also teach French. Unfortunately I have very little practice and my pronunciation is terrible. If you want to help me ... Write me)

Hello Katya and welcome to italki,

A nice introduction, if you are talking about something that continues from t he past until now we use the present perfect. (have/has + past participle /3rd form)

All the best

Bob

First record entry

It's my first record entry in my notebook.
My name is Katya. My full name (full name refers to your first name and your surname, which may also include you middle name) is Ekaterina. I'm 21 years old. I live in Moscow for a long time.
I love travelling and so I want to learn English. I also teach (do you teach French? Or, learn it?) French. Unfortunately, I have very little practice and my pronunciation is terrible. If you want to help me ... Write me)

Regarding your name, in this context, you can write in this manner;

 My name is Ekaterina or Katya for short.
Or,

 My name is Ekaterina and the diminutive version is Katya.

Great effort, feel free to write to me if you got any further queries. Happy learning! =)