middle name

In the western world it is not unusual for people to have two or more middle names.

You could add Gladys before or after Mei Yee as another middle name, so it can be:

Lily Gladys Mei Yee Chan, or
Lily Mei Yee Gladys Chan.

One thing to bear in mind is not to use names on your formal documents (such as school report cards, employment letters, official certificates etc.) which are different from the legal names (i.e. names on your HKID card, passports etc.), otherwise you may have to prove your identity when you need to use those documents.

您好，我推薦您一個非常不錯的英語學習網站，里面有很多非常不錯的學習資源，您能從中得到不少幫助：

http://www.hkenglishstudy.info

祝您好運!

You don't seem to understand what middle name is.

Technically speaking (the origin of) middle is a "fomral" name in Westerner's birth certificate given by their "mother side" or "god parents"

The given/first name is givne by their "father side".

This is how come westerner has a First Middle Last/SurName format.

Thus if you already have your "Lily" in your birth certificate/Legal ID and with the Chinese Name, I would not suggest you add another name to it. It is both a legal and valid ID issue, middle name is not fashion.

Practically, Westerner (USA mainly) only retain the middle name for formal IDs. In daily situation, the middle name is retracted to become initial(s) only just to be more clear if people are called the same First Name and Last Name. This becomes a convention.

e.g. John H. XXX, John C. XXX of the same first and last name.

As for you case. My suggestion is:

Lily Mei-yee Chan or Lily Mei Yee Chan
(depends which format is on your legal ID)
Lily M. Chan
(use in general name input)

As some already said, if you "added" a name, you will have to go to the Govt's ID registery to process it as a legal name before you can use it for formal use.

One addition note: For people without an English name in their birth certificate/legal ID. e.g. Chan Mei Yee. The appropriate way to present/apply your name is First Name: Mei, Middle Name: Yee, Last Name: Chan. or First Name: Mei-yee, no middle name, Last Name: Chan. Try to avoid First Name: Mei Yee, Last Name: Chan because Westerner (their system or thinking) may not be unable to process a name with a space. For the mainland Chinese, you will notice their Chinese given name are "one word" spelling: Meiyee Chan.

e.g. Jintao Hu 胡錦濤

If you wish to add a middle name as what you said, you have to check the following:

What is the name in your school certificate (primary, secondary)? If it carries Mei Yee, you have to retain the name Mei Yee to avoid further complications.

2010-03-25 09:32:29 補充：
What is the your name in the birth certificate? If there is no Gladys, then ask Immigration Dept to see if you need to change the name in the birth certificate at the first instance.