Well, I think there are a couple separate issues here (though ofc as with anything there are probably others I've not thought of:
Issue 1: An alt's motivations (and this alt may or may not be in any way connected to your other character(s)): In this situation, I think it is pretty easy to have an IC reason for whatever you are using the character ooc for. Some people, of course, prefer to make sure their characters only work in the other direction (what the character would do is what the player does with them). If you are planning on a character being one you RP with from the start, though, it's fairly easy to incorporate what you would like to do with that character into the concept.
Issue 2: Sort of different, but not always unrelated to issue one, is what such an alt's relationship with your other character(s) is. This is commonly handled as hirling, friend, family, etc. I would take a look at what your concept of the character is first, and decide which route to go down. (For example, if one is Amarr and one is Caldari, the family route would take some slightly more exotic background than the hirling route.)