If you start a new Profile under a new name while the old one still remains open, then all booking attempts, or searches of your Profile by a Service Provider, will show a figure in brackets after the name to indicate that the name is an alias - the figure will show the number of aliases - and the Service Provider can then check the profiles of both aliases, including all Feedback on both.
If you remove the old Profile completely then it will disappear, along with all its baggage, and you will simply have a Profile under the new name