All that we can currently conclude is that the picture on the door looks like the Razor, and appearing similar doesn't prove that it is, in fact, the Razor.
However, if we were to continue on with that line of logic, then we also cannot conlcude that the woman in the picture is, in fact, the Night Mother, only that she looks...wait a minute...we don't even know what the Night Mother looks like.
Therefore, to assume that the woman is the Night Mother based on assumed appearances and NOT conclude that the dagger is the Razor when we know what it looks like is a selective application of logic.
___TWM of J
spoiler:
Spoiler If you finished the DB quests, you'd know what the Night Mother looks like.
I think it's safe to assume that the woman in the picture is the Night Mother. Remember all those "family" references that Lucien Lachance made in his little intro speech?
I remember him saying something about their "dark family," the Night Mother being an "unholy matron", and something about the DB being born from the Night Mothers' womb. And c'mon, I mean, her NAME is the Night
Mother.
So who else would the woman in the door be besides the Night Mother? She's holding a child and the other children are reaching out to her. The child she is holding is probably the Listener, who she obviously favors most, and the other children are members of either the Black Hand or lower-ranking members of the Dark Brotherhood.
I don't think there's much to it as far as meaning. It just symbolizes that the Dark Brotherhood was born from the Night Mother, as Lucien Lachance said in the game.
edit: As for Mehrune's Razor being in the picture, it does look a lot like it. Considering that the Razor has a lot to do with the DB's history, and is a very suitable dagger for their guild. It might be there to symbolize the Night Mother's power or something.