10 is such a small number for modern computers that it hardly matters at all which approach you are using.
The soul is dyed the color of its thoughts. Think only on those things that are in line with your principles and can bear the light of day. The content of your character is your choice. Day by day, what you do is who you become. Your integrity is your destiny - it is the light that guides your way. - Heraclitus
Aside from performance, do you need to keep the data around, or not? It seems to me that if you create 10 objects (which is not a big deal, as Ilja says) you still probably want to put them in a List of some sort (or maybe an array) - don't you? Or if you don't need a List, then you probably didn't need a List of Strings either. It seems like there are two separate, unrelated questions here:
1. Do you want to represent the data using only Strings, or using objects of some custom class that contains a name field?
2. Do you want to put multiple objects in a List, or an array, or can you just throw each object away after you're done with it?
As usual, performance seems to be a relatively unimportant part of the problem here.