The proper identification is an entomologist, which is a person that studies insects. However, if you want to be very technical, a person that collects actual bugs, which are a type (or class) of insect, that person is called a hemipterologist.
A person who buys and sells bugs would be a bug dealer. At least that isn't illegal yet. Just imagine if cops tried to arrest you for being a bug dealer. They would RAID your house.
A badge collector.
A paper collector
A bibiliophile.
A deltiologist is a person who collects poststamps as a hobby.
The terms are lessor (the person who collects the rent) and lessee (the person who is paying the rent).
That's an entomologist.
A person who collects beetles is a coleopterist.
a strawber.
Bibliophile
collecter
supernatural
A cravatologist.
A badge collector.
A paper collector
a button collector
A gem collector
A car collector?