I'll be avoiding spoilers of actual events here.
The squadmates do not change based on your Paragon/Renegade/Charm/Intimidate scores alone. What matters is what you do to them and say to them.
Ashley - Some upper responses encourage romance. She can be slightly affected by your morality and turned more 'Paragon'. While romance continues into future games, the morality doesn't.
Kaidan - Some upper responses encourage romance. He can be slightly affected by your morality and turned more 'Renegade'. While romance continues into future games, the morality doesn't.
Liara - Some upper responses encourage romance. That's it really. She feels high attraction (romantic or otherwise) to you regardless.
Wrex - Doing a sidequest for him helps in his affection towards you in ME1 and this is also recognized in the script for future games. There is a Paragon/Renegade check with him at some point.
Garrus - Doing a sidequest for him can change how he is affected by your morality. However, this doesn't continue into future games.
Tali - Doing a sidequest for her can slightly change her affection towards you in future games.
~~~
Basically when it comes to affection, there isn't much. For Ashley/Kaidan there is the romance. For Liara there is the romance. For Wrex there is the sidequest. For Garrus the sidequest barely counts. For Tali there is the sidequest.
You don't need to worry about (at least most) characters having affection for you in ME1. There's one partial exception, but I won't get into that for spoiler reasons.
ME1 doesn't really have much of an affection system. They mostly gladly follow you regardless.
ME2 has its own thing called Loyalty which *does* matter, and affects ME3.
ME3 then has more unique experiences, choices, and consequences that affect how characters view you (but nothing like the Friendship/Rivalry deal in DA2).
~~~
I dunno why you're worried about character names though. You get the first 2 at the start, then the next 3 shortly after, and the last 1 on another mission. It isn't exactly spread out or spoilerish. ME1 has been out for several years now.