Yes and no. It is the same Time Lord, who will have the same memories and basic ideas of right and wrong, good and bad etc.
However, the way those beliefs manifest themselves will be different. All the Doctors have had the same beliefs, but the way that they have tried to do good have differed quite significantly. There will also be individual tastes, such as one incarnation of a Time Lord may not have the same tastes in clothing, food, music etc. to his/her predecessor or successor. One incarnation of a Time Lord may speak differently to his/her predecessor/successor (eg. the Sixth Doctor was very loud and outspoken, whereas the Seventh Doctor was more quiet and reserved).
A Time Lord will consider other incarnations of him/herself to be both the same individual that (s)he is, but will also consider them different, based on their individual personality. Sometimes a Time Lord may even have preferred previous incarnations of him/herself.