I’m adopting my husbands children from previous marriage.

It’s a great decision that as a family you have decided to follow Sikhi. Sikh religion and it’s principles are based to lead a successful family life. Making contemplation of Guru-Shabad as the common goal for both husband and wife is the key to happy family life.
Yes. Children must use Singh and Kaur with their names. This will ensure that they also feel a change towards good.
For a name change from a legal perspective, you must consult someone who is legally an expert in such matters.
Thanks.