I LOST MY HUSBAND LAST YEAR, FINALLY FOUND A MAN TO MARRY BUT WANTS MY CHILDREN TO BARE HIS NAME INSTEAD OF MY LATE HUSBAND

"I lost my husband last year, finally found a man to marry but wants my children to bare his name instead of my late husband

Am so happy, at last i finally found someone who accepts I and my children, he is richer and provides I and my kids every need and also shows me so much love even more than my late husband did, the truth is, I feel more comfortable with this man. He even open up a supermarket for me.. 

He asked to marry me in which I have accepted, the problem now is, am disturbed on the fact that he has asked to marry me on the condition that we remove my late husband's name from my children's names and replace it with his own name..

I have tried talking to him to wait so that, I consult my people first because my late husband had fully paid my dowry. But, he insist we shouldn't inform them and that he has people in the government who can quickly switch the names without any delays or complications. Actually, I don't know what else to do because am afraid to loose him. I'm a 33year-old woman with 3kids. Age 4 a girl and 2year-old twin boys. I fear i might not find another man to marry me. I'm still a young woman whom also deserves a sweet love life. I also see that, changing the names is of no big deal since we are getting married to make one big family. 

Pls kindly advice me on this.

She wrote..