Everton had to name a 25-man squad by the end of today according to the new Premier League rules. According to the rules, the squad can only be modified during the January transfer window once it is submitted. The rules also state that there must be at least 8 "home-grown" players (must have spent 3 years in an English or Welsh club between the ages of 16 and 21) in this 25. There are no restrictions on players that are under the age of 21.
Luckily, Everton has a lot of home-grown players and a lot of youth so they had no trouble to get under the quota. All of Everton's registered players are eligible to play this season (and we only had 21 players over the age of 21). All information was taken from the Everton website.
Here's the squad (with "home-grown" players italicized):