Yes, it is possible for a mother to give a surviving twin the same surname as his deceased twin brother. The decision of what surname to give to a child is usually at the discretion of the parents, and there are no strict rules or legal restrictions in many places regarding this matter.
If a family has already chosen a particular surname for their children, it is common for the surviving twin to share the same surname as the deceased twin as a way to honor the memory of their sibling. This choice can provide a sense of continuity and connection within the family.
However, it's essential to consider cultural and legal practices in your specific region or country, as some places may have different naming conventions or regulations. Additionally, individual circumstances and personal preferences may influence the decision, so it's always a matter for the parents to decide what feels right for their family in such sensitive situations.