Does it have a caudex? If so then it may be a hybrid of dregei.

Try this site to see if it looks like yours:

Weltonensis (a B. dregei look-alike)

I agree, I used to have this too.

Well, the leaves look the same, but no caudex shown, a new word for me. Very fragile branches. I received an email in regard to this plant...they said that it was hybridized with Dregei and sutherlandi..It definitely thrives in cool temperatures and blooms..50 to 60 degrees...tolerates warm temps but no blooming then. Here are a couple of pictures of it.

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Your pictures look more like a trailing begonia - like Tangier or Tiny Gem. Have you got a larger picture?

Tangier

Tiny Gem

I don't know how i can make it any larger. I came close to the bottom one to show there was no caudex..yes, it is trailing or cascading type...don't know anything about Tangier or Tiny gem, though the names sound familiar...perhaps they are of the dregei and/or sutherlandi variety? If so, then that may be the reason why they look like them..like i said in my op , a begonia specialist emailed me and said that it was the hybrid of Dregei and sutherlandi.

Maybe sutherlandii hybrid.