Having a "Romy" doesn't make a whole lot of sense, unless you want it to be a part of the crew, and then I would make it a slave to the ship's AI rather than run the risk of letting it develop its own AI and muck with things, and with Virus running around, this is even more important. I've only seen a dozen or so episodes, so I'm no expert when it comes to hacking the show's mistakes into pieces.
The AI for the ship's human interface can be anything, and can be anything to anyone. Maybe the captain likes to see his mother, the first officer likes to see a paper clip, and the weapons officer wants to see a Borg. Ok, so when the AI addresses multiple people at once, it might be a little confusing, so you'd want a single avatar and to hell with preferences.
Depending perhaps on certain circumstances, your avatar might "wear different clothes". It might wear more martial clothing and have a different tone of voice when at battlestations, have another "mood" when doing unreps (underweigh replenishments, basically ship-to-ship transfers of supplies or fuel), and might even have a different "mood" for when the ship's in port and it's after normal duty hours (most people have left for the night).
More important than an avatar - which is only useful as a human interface device, remember - is being sure that human and AI can understand each other. If the captain says "forget it", the AI needs to be able to tell if he means this literally (delete all data on the subject at hand) or figuratively (I don't want to talk about it right now, or it doesn't matter). The Holy Grail of AI is to be able to speak to it like I would speak to you, and it would be able to determine the meaning from what was said (which is a hard enough job that even real people don't get it right all the time).
At lower levels of sophistication (generally lower TLs) the human will have to rely on predetermined command words. Maybe he has to start all commands by saying "Computer" in a clear voice, then has to pick a general action from a "menu" of possibilities, then give a more specific command. Examples: "Computer, weapons, all, fire at target number 3, fire.", or "Computer, look up, data relating to item: hedge row tactics, look up." or soemthing along those lines. A less sophisticated computer would have fewer such recognizable commands, a better one would have a number of aliases for commands, so the human wouldn't necessarily have to remember all commands, or could create his own.
The fun comes when your players start shouting commands at the computer and forget all about the proper syntax they have to use to get things done. The results could be the irritating Majel Barrett voice saying their command does not compute, or could be activating a function completely unintended. Note that you don't have to make up valid commands, write them down in a book, and make your players memorize them all (which their CHARACTERS WOULD have to do), just telling them that the computer only understands Pidgin and requires all commands be prefaced with "computer" is enough. (Mind you, I'm not saying Majel's voice is annoying, just when that stupid computer says it can't do anything, THAT'S annoying.)
