Have you read the docs for DBD::Oracle? It shows how to use the service name to connect. Although, to be fair, it calls it the SQL*Net 2.x connection descriptor. That's what a service name is really; a connection descriptor. The following code is totally untested. (Be sure you have your usual Oracle config in place environment variables set, yadda yadda yadda...)

use DBI;
my $db_user = 'Scott';
my $db_pass = 'Tiger';
my $service_name = 'foo';
my $dbh = DBI->connect("dbi:Oracle:$service_name", $db_user, $db_pass)
+;
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