"My name is Mark and your name is Victoria."
Translation:Мене звуть Марк, а вас звуть Вікторія.
No, that would sound a bit weird. If the names were the same, you'd use "і"
My name is Mark, and his name is Mark, too. Мене звуть Марк, і його теж звуть Марк.
If the names are different, you use "а".
My name is Mark, and his name is Mike. Мене звуть Марк, а його - Майк.