The name of the phobia related to the fear of dental surgery is Odontophobia. See Web Links for a list of all phobias and their names
The closest "official" phobia would be Odontophobia; fear of dentists.
However, a closer word might be honondasdontiaphobia; literally fear of losing teeth.
Dentophobia.
Denthobia
Tomophobia
Fear of teeth (or dental surgery) is called Odontophobia
the fear of teeth or dental surgery: Odynophobia or Odynephobia
Both dentophobia and odontophobia relate to the fear of dentistry and receiving dental care.
Fear of a toothbrush is generally grouped under Dental Phobias. Dental Phobias relate to irrational fears of anything related to dentistry (dentists, dental tools, dental offices, dental hygiene, etc). EDIT: I didn't want to remove the others person's suggestion so I'll just type below :-) a fear of toothbrushes, or in fact, to clean your teeth is 'Odontarrupophobia'. You do not need to group it under dental phobias as from a psychological point of view every fear to do with 'dentaistry/dental/dentists is rooted in something different and therefore called something different.
The irrational fear is called a phobia; the experience or object that triggers a phobia could be called a phobic experience or object.
the only phobia of the fear of crickets is crickephobia
Bebuphobia...that is the fear or phobia of blueberries.
To have a phobia is to have a fear.
Mud Phobia is the phobia (fear) of mud. Its called mysophobia, myso meaning mud and phobia meaning fear.
Atychiphobia (kakorrhaphiophobia, fear of failure, fear of failing, failure phobia).
Theophobia- the irrational fear of a god or deity. Remember its only a phobia if its an "irrational" fear, a normal healthy fear is not a phobia.