This depends upon your location.  While I respect a strong referral
that a patient has received elsewhere and try to respect it, you are
sometimes better with a restorative dentist and surgeon who know each
other and their way of operating.  Remember that both will have a hand
in the process; the surgeon in placement of the implant fixture and any
necessary grafting; the restorative dentist in placement of the abutment
and crown (the abutment is the interface between the fixture and the crown).
    With single-tooth replacements things are usually pretty routine.
However, because of the impacted tooth and the fact that the implant
will be near the front of your mouth, it is important that the surgeon
and restorative dentist are on the same page with this, as there are
potential cosmetic pitfalls.
    Generally, if a patient prefers to work with a particular specialist,
unless I have a particular reason to object, I will go along.
    Yes, you should expect to be charged a consultation fee by both
dentists, though of course individual office policies may differ.
    BTW, there is no recognized specialty in "cosmetic dentistry".  There
are academies, study clubs, and lots of lectures out there, and there
are well-known experts who cater to "the stars", but IMO no one should
present themselves as a specialist in cosmetic dentistry.

Steve

    Good points.

Steve