I hope I did understand your problem. Here is my sample code. Kindly check it if the flow and output fits to the solution of your problem. If it didn't, I hope it can give you some clues. Just like Javafan said check each word of "my_name" if they all exist in one of the string of database "db_name".

#!/usr/bin/perl -w

@my_name=("Acidovorax","JS42");    #name to be searched...
                                   #...split by term/words
@db_name=("Acidovorax sp. JS42",    #data base of names in array
          "JS42 Acidovorax sp.",    
          "JS42 sp. Acidovorax",
          "JS53 sp. Acidovorax",
          "JS42 sp. Axidovorax",
          "JS42Acidovorax sp. "
          );

my $ctr;
#----compare strings in $db_name 1 at a time
foreach my $db_each (@db_name){            
   
   #----search each term/word of @my_name in $db_each
   foreach($ctr=0; $ctr<=$#my_name; $ctr++)   
   {
          #----if a term/word not found break the loop
       last if($db_each !~ /\b$my_name[$ctr]\b/i);  
   }                                                
   #----this will be true if inner foreach didn't break
   if($ctr==$#my_name+1)                            
   {
       print "$db_each\n";       #print the matched name
   }
}
<>;
[download]

I have mention the "term/word" in the comment. It might be that two words in your "my_name" is considered as one term or two or more words separated by space.

The code above does not support if a word should exist 2 or more times in any order. example: my_name = "high class bacteria f7-52 high fever". Just mentioning this condition for more flexibility to your program. It's still up to you.