Hey Mark -
What sort of error are you receiving?
The approach you described above is certainly one way to go, and probably preferable. Keep in mind, depending on when/how a "Person" is being created, you would want to account for null values in your FirstName + ' ' + LastName calculation. But would definitely need to see what your error is to diagnose potential issues.
Alternatively, you could also create a microflow that can be used as a sub-flow any time the First or Last name is modified and then committed to your db. Lastly, another approach could be a calculated attribute on the Person entity that simply looks at the value of the FirstName and LastName and returns the concatenated value. Again, want to consider the possibility of a null value for both attributes.
Just some other options worth mentioning.