i have 2 daughters out of zina from a non-muslim, now i am married to a muslim and accepted my 2 daughters and they are using his family name. is these accepted?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

If you mean by “accepting the two daughters” taking care of them and treating them kindly, then your husband will be rewarded for that by Allaah The Almighty. However, if you mean adopting them and attributing them to his family, then this is prohibited because the two girls are illegitimate children and it is known that in Islam the illegitimate child is attributed to his mother and her family with all filial rulings (related to her and her family) including being a Mahram, guardianship, inheritance, being an Asabah (a relative who is entitled to inherit the residue after those who have fixed share in the inheritance) etc.

For more information, see Fataawa 102092 and 84788.‏