I think "de origen" sounds better because your name does not relate to a Russian name, but it is a derivation. In your idea about your mother was a kid/young. The imperfect tense in the past fits better because your mother kept in her mind your name for a time, but you did not know whether finished at the end your mother called you Tanya. In Spanish, the imperfect tense in the past is called "Copretérito". In my view, "En la actualidad," I am not sure if your mom had changed her name, it would sound well. So, I suggest using "Sin embargo" because it is a contrast. The most difficult in Spanish is to write the kind of gender of each word. It is essential to be careful because in Spanish the gender gives mush and specific information. Although for now, it is ok. Well done.

Hola, cuando escribimos países deben escribirse en mayúsculas por ejemplo: Estados Unidos. Mi madre eligió mi "nombre". En actualidad puede sustituirse por "Actualmente". Saludos Si quieres practicar tu español, estoy abierto a sesiones uno a uno.