Naming of bicyclo[2.2.1]hept-5-ene-1,4,5,6-tetramethyl-3-bromo-2-ethyl carboxylate
The individual parts of the proposed name are correct; however, their order of citation in the name is wrong.

The name of the parent hydride is ‘bicyclo[2.2.1]hept-2-ene’. Note that the ending ‘ene’ receives the lowest locant possible (here: ‘2’ since the bicyclic ring system is numbered starting with one of the bridgeheads).



The principal characteristic group is expressed by means of a suffix, which yields the name ‘bicyclo[2.2.1]hept-5-ene-2-carboxylate’. Note that now the characteristic group receives the lowest locant possible (here: ‘2’), which
is cited immediately in front of the suffix. Thus, the locant for the ending ‘ene’ in the functionalized parent hydride is changed to ‘5’.



The other substituents are cited as prefixes in substitutive nomenclature: ‘3-bromo-1,4,5,6-tetramethylbicyclo[2.2.1]hept-5-ene-2-carboxylate’



Finally, the name of the ester is formed according to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), by placing the ‘hydroxylic’ component in front of the name.


  P-65.6.3.3.1 Monoesters
  
  Monoesters formed from a monobasic acid and a ‘monohydroxylic’ component are named systematically by placing the ‘hydroxylic’ component denoted by an organyl group (alkyl, aryl, etc.) in front of the name of the acid component expressed as an anion derived from the appropriate acid (…).


Therefore, the preferred IUPAC name (PIN) of the compound given in the question is
‘ethyl 3-bromo-1,4,5,6-tetramethylbicyclo[2.2.1]hept-5-ene-2-carboxylate’.