Should I choose a particular name or 'handle' for CW traffic? The answer to this question is 'it depends'. The following points may be worth considering.
The first and most straightforward name is simply the name that you are used to from relatives and friends. Even if it is a little longer you will not suffer any disadvantages. If you use e.g. 'Thomas' instead of Tom you will not really loose a lot of time. After all it's a hobby and nobody counts the split seconds. If you have a radio name for other modes, just use it for CW, too, for the sake of remaining consistent.
It is an advantage if your name matches your call sign. However, by now it is not uncommon that names reflect an ethnic background and not a living place. In this case it may be an advantage to expose such a 'foreign' name because the qso partner might be happy to use the language that the name points to.
It is an advantage to be consistent and not use many names at the same time. A common deviation from this general idea is to have a local name to be used for co-nationals and an international name. This makes sense if you feel your name sounds too exotic for international use. If you make up a radio name, be sure to check the Internet in order to find out whether or not your handle is not loaded with negative meanings or with misleading associations.
If you have the bad luck that your name uses special accented characters, dieresis, umlauts and such international partners should not be challenged with special morse code chars like --.--, .--.-, ..--, or such. A near-Ascii representations makes sense in this case.