How old is your child/ren?
With young ones, you should introduce yourself as you are - that is mummy and daddy.
Older children can be different, but even so, when I made up my book for DD2, who was nearly 8, I definitely called myself mum, but used my first name as well. I was introduced as her new mum X, then she called me 'Mummy X', then finally she dropped my name and simply called me 'Mummy'. Because of her age and knowing her birth mum as mum also, she did need that time to call me 'Mummy X' at first, but even with 8+ year olds, they usually become comfortable with 'mum and dad' quickly. DD2 took only a few weeks weeks to drop my first name entirely.
The only child I did it differently with, was DD1 who was 10 and a half, because I was told by her FC that she didn't like the word mum very much. Therefore I simply used my first name, and we drew a distinction between 'mum' and 'parent'. However, her situation really isn't common. It's very unusual not to say mummy and daddy.
I would bear in mind that your child/ren should have been being prepared for adoption for a time already. Social workers and foster carers usually talk about it to the children in terms of 'finding a new family to live with forever' and do say 'your new mummy and daddy'. I expect that unless your children are much older, they will have been being told they are going to get a new mummy and daddy to live with forever. If they were having difficulties with the idea of a new mum and dad, it should have been picked up at that stage.
If you are unsure, I would ask the childs SW/the foster carer/s, because they can tell you how the children have been prepared, how they're talking about adoption to the child/ren, and what the child themself has been referring to adoptive parents as. Then you can introduce yourself in the way that the child has been thinking about you/ told about you.
But unless you have an unusual situation, I would call yourself mum and dad, and with an older child, you can tell them your first names as well.
You aren't replacing the role their birth parents have had and will have in their lives, but you are most definitely becoming their mum and dad. And children themselves often really want that normality of having people to call mum and dad, and being like other children.