I liked when our past came up in the first Mass Effect, or even just to jump-start some thoughts on who your protagonist is. Playing a Colonist, for instance, you can go with a Shepard who's very antagonistic towards Batarians. Maybe not particularly creative, but it still gives your Shepard some character that you can then add on to.
If it's not going to be referenced in dialogue or open its own quest(s), however, I'd probably prefer to not have a selectable background story. Guess it depends on how much focus there'll be on the new setting and our place in it... Might not be a whole lot of room for Ryder's background.
I'm confused as to why people are using the name Ryder. It was on a dogtag you say? Fantastic, but shouldn't a soldier going to action be wearing said dogtag? Leaving it behind defeats the purpose, no?
Its purpose was, we assume, to hint at our protagonist's name in a sneaky manner. The trailer wasn't a 100 % accurate depiction of what happens in the game
don't take everything too literally 
I thought this game was taking place during ME3?
ME:A 'tak[es] place far away from and long after the events of the original trilogy', so not during ME3, no. However, as Hanako Ikezawa points out above, the journey to Andromeda might well start at any point in time, during, after or even before the Reaper War.