I have tried to incorporate softened cream cheese with pumpkin puree and it's never fully incorporated - small bits of cream cheese are left in the mix. How can this be prevented? I've tried 2 different brands of cream cheese and these bits happened both the times.
When mixing cream cheese with softer or more liquid ingredients, you first need to make sure both things you're mixing are softened and smooth.
Even room temperature cream cheese is sometimes hard to mix. I usually microwave it in a glass bowl for 30 seconds then beat it until it is smooth. A food processor or electric mixer will make this easier.
In a separate bowl, beat the pumpkin puree (or whatever else you are mixing in) until it is smooth.
Now take a few spoonsfull of the pumpkin puree and add them to the cream cheese. Mix until smooth. Add more of the purée, mix. Eventually it will all be incorporated, or if the cream cheese mixture becomes liquid enough, you can add all of it in.
If you're mixing the cream cheese into something more solid like almond paste, reverse the process and start with a couple spoons of cream cheese in the stiffer ingredients.