Several. If they have you on their friend list, they will see you logged in no matter what character you are playing on. The friend list works on the account level.
You can also send tells to people with just their account name. If you use "/tell @account <message>" it will go though. Tells are also on the account level, so they will go through to you no matter what character you are on as long as you are logged in.
If you look at the Social screen, you will see Friends, Team Settings, Ignore, and Search. Using the Search tab, you can also see the person's rank and fleet (if any). Due to this capability, you can often find yourself getting a random recruiting PM. The very day after I created my first Caitian, I was shooting Borg on Defera, and someone all the way at ESD started sending me recruiting messages. Strange as this may seem, there actually are people who have nothing better to do with their time than continuously browse the Search page for unfleeted low levels.
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You can also send tells to people with just their account name. If you use "/tell @account <message>" it will go though. Tells are also on the account level, so they will go through to you no matter what character you are on as long as you are logged in.
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