Hi seedly! What happens to my mother’s hdb when she passes away? Since her hdb doesnt have my name what will happen to it?

Your mother need to write a will to transfer the HDB to you, else it will need to be Administered when she passes on without a will, and will cost more money to transfer. Since you already have a HDB, you will then be required to sell your mom's HDB, since you can't own 2 under HDB rules.