It looks to me like an echeveria, and has grown that way b/c it doesn't get enough sun. Can you get a grow light for it? That would be the first step, imo.

ez

Unless you can find significantly more sunlight, I'm afraid there isn't much to be done. Certainly, beheading would give you a fresh start but without the sunlight you'll be back to square one. The soil is too rich for this succulent; something more gritty would also help, like adding 50% perlite.

As already said - much more light is a must.

You could easily just twist off the growing shoots and pot them up, but there is no point in doing it unless plants can get more light. Pictured plant has been growing with insufficient light for a while (much longer than a month).

What is the light situation - you said apartment is even darker than previous place. Can you/are you willing to get supplemental lights?

Yep with succulents, I think of long branches or undesirable-looking branches as a new plant to pot up, so I don't really mind sometimes if a particular plant doesn't grow the way I wanted it to. In this case, I could totally see 2 plants from this one, growing in same pot since it looks like their root system isn't that extensive.