Why not: 'Miaj gepatroj nomigis min Sofia'? (My parents made me named Sofia)
Esperanto can be confusing with those three verb forms: -i. -igi and -iĝi. I'm myself still a komencanto, but I try to explain how I have understood it.
Let's first take a verb with all three forms:
esti: to be, something is/was/... something: "Mi estas komencanto." = "I am a beginner."
estigi: to make something being something: "Tio por mi ne estigas diferencon." = "It makes no difference to me."
estiĝi: to become being something: "Silento estiĝis." = "It became silent."
Now, there are a lot of verbs which aren't meaningful in all three forms:
nomi: to name, to call someone or something by a name: "Li nomis sian filon Petro." = "He called his son Petro."
nomiĝi: to become called by a name: "Kiel ŝi nomiĝas? Ŝi nomiĝas Johana." = lit. "How has she become called by a name? She is called Johan(n)a." meaning "What name does she have? Her name is Johan(n)a."
An -igi form of "nomi", "nomigi", would mean "to make something being called by a name" but since that is essentially the same as "nomi", the simpler one is used. One could think that "nomigi" would mean "appoint (to an office)" but in Eo, one uses "elekti" both in cases where you vote and someone appoints someone.
I hope I got it right and this helps you.
(Vidu http://www.reta-vortaro.de kaj serĉu vorton "nomi".)