To me this looks like a case for enums.
There's a Enum Creator Wizard in the menu Playmaker > Addons > Tools, but it's a good idea to understand a little how they work. Enums are basically a list of variables where one is true, and the others are considered false. Multiple choice is also possible, for which you need to google [EnumFlags] and [System.Flags].
By default, they are made exactly for this purpose: showing a dropdown list, where one thing is selected. Try this out: As usual, scripts work anywhere in asset folder. Make a new file, named "MyCharacters", and put this code into it. Or just download my example.
namespace MyNamepace.MyCharacters
{
public enum MyLittleEnumList
{
Alice = 1,
Bob = 2,
Charly = 3
Dwayne = 4,
Erica = 5,
Finn = 6,
Gerald = 7,
Harry = 8,
}
} // END Namespace
This creates your new enum list. The numbers behind are optional, but you want this to make it a bit more robust. If you don't assign them, they are given at runtime, which means that when you later on delete Alice, then Bob becomes 1 and Harry becomes 7. A player who plays Erica will then play with Finn and so on. Also, you want to keep the numbers glued to the character, once things go live, but you can change the order around as you want.
The name of the file must match MyNamespace.<here>. The purpose of doing it like this is that it creates a submenu <MyNamespace> where you can keep all your enums in one place. If you never ever have more than one, and you swear to your chosen deity, you can simply leave the "MyNamespace." away. You generally want to use a namespace, because to find the enum often involves navigating through lists, and that makes them easy to find and keeps them all together.
You have now created a new enum list that has these character names as possible options. To wrap your head around this, think of this as new variable type. E.g. float is the type and "myFloat" is the individual variable that then contrains one float. Likewise, <MyLittleEnumList> is the type, and then you need, as usual create your actual variable in the FSM, e.g "activeCharacter".
Simply set it to Enum, and then click on the newly created variable, and in Enum Type, navigate the list to your namespace and et voila, there's <MyLittleEnumList>. You can then treat this as any other variable, set it to "Bob" or whatever.
If you end up having more enums, you can rename the file to "Enums.cs" and likewise the namespace line as e.g. "MyGame.Enums". You can then simply append any number of enum definitions as you like. If you want to reference them anyway, you access them as MyGame.Enum.MyLittleEnumList, i.e. Namespace.File.EnumlistInFile.
Hope that helps.