During the first episode of David Tennant, The Christmas Invasion, Rose returns to her family for the holiday as the Doctor is going through his regeneration process. As Rose has only known Christopher Eckelson, she sees the Doctor changing appearance as the doctor becoming someone completely else. During the time that he is trying to recover, Rose cries to her mother about how the Doctor left her and replaced himself with the “stranger” that laid in bed.
During the tree attack, Rose whispers to the Doctor to help her, he wakes up to rescue them and then explains to Rose, Mickey, and Jackie that he thinks that his regeneration is not going right and that something bad is coming.
During the remainder of the episode Rose is hesitant around the Doctor and is angry that he is leaving her alone. When he finally awakes and defeats the Sycorax, he asks her if she will continue to travel the stars with him.
Just like normal people, we get attached to others and so when they change it is hard to come to terms with. Whether or not Rose knows that the Doctor regenerates like that is something I do not remember, but if she had not this would explain why she is so upset when Tennant takes over the role.