Why does this sentence mention name?

海岸には５０８名の女の子がいます。

First, the best way I can translate this is: As for on the beach, there are women of 508 names.

This tells me that I am certainly not reading this sentence correctly. How is this sentence supposed to be read?

海岸には５０８名の女の子がいます。

名 is also used as a counter for people, so the sentence reads:

508 girls are at the coast.

http://en.wiktionary.org/w/index.php?title=%E5%90%8D&oldid=18643011

Contents
3 Japanese
3.4 Counter

Would any of these be wrong?

海岸には５０８人の女の子がいます。
海岸には５０８にんの女の子がいます。
海岸には５０８じんの女の子がいます。

It is a little complicated and let me unclarify for you, lol.

名
1. is used when the names of each person in the group of people can be identified.
i.e. How many students took the test? 200 mei desu.
2. At a restaurant a group of customers is asked, "nanmei-sama desuka?" how many people? (never nan nin desuka? You might walk away upset being treated rudely.) You reply 3 nin desu, not 3 mei desu.
3. More specific than 人. The capacity of an elevator is written 10 mei max.
4. can be used in the context of lessor societal class order. Also dependent on who is reporting to whom of how many in a group.
There were 4 criminals=犯人は4名いました。

人
1. is used to report just the quantity of people.
Normally they can be interchangeable.
Confusing, isn't it?

hajime gakusei,

"Jin" is the reading for the kanji 人 when you are talking about nationalities and other characteristics of people. For counting the number of people, "nin" is the reading to use.