There seem to be at least two reasons that no one so far has answered your questions.
1) Food names -- the older foods in particular -- differ greatly from one region to another.
2) おぼろ has become increasingly unpopular during the last few decades; therefore, the younger members may actually have never seen or eaten it.
" Are there any other common words for [桜]{さくら}でんぶ?"
No, not that I know of -- except for plain でんぶ. I grew up calling 桜でんぶ just でんぶ without adding the color name. In fact, I could not recall ever seeing でんぶ in any other colors besides pink. I have lived half of my life in Tokyo and the other half in Nagoya.
"I read other places that おぼろ and そぼろ is used for 桜でんぶ, but are these words common?"
To me, the three food items that you mentioned are all different things.
おぼろ comes in much larger and heavier flakes than でんぶ does. おぼろ feels "wet" while でんぶ is pretty much dehydrated. One could arguably say that the two taste pretty much alike because they are both made with white-fleshed fish like red snapper.
I have not seen おぼろ in more than a couple of decades, honestly. Grandma used to make it and she was the last person to do so in my family.
Moving on to そぼろ, it usually refers to ground pork or chicken fried and boiled in soysauce and sugar. It is still very popular and I am sure you have seen it in convenience store bentos covering the rice with eggs cooked the same way.
"Is the word 桜でんぶ widely known in Japan? When I ask friends about 桜でんぶ, many don't seem to know what I'm talking about, but maybe this is just limited to my friends."
All I could say is that the word 桜でんぶ should be widely known pretty much everywhere because I do hear/see it in the media. Your friends may be too young to know the word. I am sure they have seen and eaten it in inexpensive sushi, but it is just not something many people buy by itself, let alone cook at home anymore.
