This question comes up frequently when I'm working with clients to put together or update their estate plan. Often times the answer will be "yes" because naming the same person as your executor of your will and successor trustee of your revocable living trust will minimize expenses since the attorney helping to settle the estate and trust will only have one person to work with to address all of the issues that come up.
But beware of naming the same person as your executor and successor trustee if you live in Florida or own real estate in Florida. Why? Because in Florida your executor must be related to you by blood or marriage in order to be able to legally serve as your executor, but you can name anyone to serve as your successor trustee. (For example, if you are a Florida resident, then you cannot name your best friend who lives in New York to serve as your executor, but you can name your New York friend to serve as your successor Trustee. This is one of the many reasons a Florida resident may choose to use a revocable living trust as part of their estate plan.)
Aside from state law issues, you may simply want to name a different executor and successor trustee to provide checks and balances in settling your estate and trust. Or, if you are having a hard time choosing among your children or other relatives, then you may decide to name one child or relative as the executor and two children or relatives as the successor co-trustees, or vice versa, in order to avoid beneficiary feuds and promote family harmony.
With all of that said, if your revocable living trust is completely funded, then in most cases your estate will avoid probate, which means that your last will and testament and the executor named in it won't be needed. If this is the case, then who you choose to serve as your successor trustee will be a very important decision for you to make.