By personality, do you mean intelligence, thoughts, feelings, emotions, etc.
Obviously yes. Including ones we eat such as cows, goats, deer, sheep, even chickens. That’s why people keep them as pets. They recognize people as individuals, display preferences for people and things.
We can eat them because Ha-Shem expressly told us we can. Before that we couldn’t. Adam ha-Rishon didn’t eat fleishigs. If you don’t hold by Humash (and the aggados and kabbalah), you probably should be a vegetarian. Even ones we can’t eat (such as insects, reptiles, rodents, etc.) are still protected by halacha from being tormented or treated cruelly.