For example my mum surname is Lidia and dad's surname is Jannat. My name is Sofia, can I change my name to Sofia Lidia Jannat? In Islam they say your mum 3 times then your father. My mum is more around and close to my personality than my dad. Why should I take only his surname. My mum took care for 9 months in her belly. Now I know changing surname is haram, what about adding your mum's surname. Thanks, please also cite verses if against it.
There are no verses for what you're asking for.
Usually if a person's father was unknown then they'd go by their mother's name. Not knowing who your father is, isn't good. Islam always recommends us to distance from something that is considered shameful in the public eye.
I don't know if there are any verses against. But in essence in Islam the idea is that Prophet Adam (not Hawwa) carried all the loins (صلب) of all people. Then through each son, whomever that son was to father then their loins would get passed along that child. For all the years a child isn't born their طینت is carried by their father and his grandfathers. Only for a period of 9 months a child is with their mother.
For that the reason the main attribution of a child goes to their father. Think of a seed vs. the earth it grows in. Not the most perfect example, but you get the idea.
Having that all said, you know your father and just like a combo name. I couldn't find any narration against that, but please do your own due diligence.
The only verse in Qur'an which uses the term 'loin' is: Nisa:23 but I couldn't find much more on it.