Am I allowed to create such page name?

Am I allowed to create a page with the name Liking zone or Like zone, Like Me, Share me and such stuff ? Will my facebook page get banned?

according with the facebook tos, you are not allowed to use incentive words, to like, share etc in title, cover photo, profile photo etc.
i don't know what happens after.

Since you are "You are required to restrict access to Pages (through our gating functionality) as necessary to comply with applicable laws and Facebook policies, including our Advertising Guidelines and Community Standards." and in the Advertising guidelines the next paragraph appears: "All other ads and landing pages may not use our copyrights or trademarks (including Facebook, the Facebook and F Logos, FB, Face, Poke, Book, and Wall) or any confusingly similar marks[...]"

Basically through that logic you can't actually use Like in the page name, however, lots of pages do that exactly! If you chose to do so and Facebook decide to do some house cleaning your page and you to might be banned from Facebook. So, you can do so, just know the risk.

(For example: Facebook tells you that community pages basically belong to them, but you can still open and admin them. If they grow enough, and that has happened, Facebook just removed the admins and took control of the page.)