Was I supposed to prune this plant before this year's new growth?

I can't remember the name of this plant. I think someone told me what it's called previously on this forum.



As stated in the subject line, should I have already cut the old flowerheads off before the new shoots?

As you can probably tell, I don't know much about plants and I don't know how this works but I'm trying to look after them!

Thanks very much.

 

Thanks very much, shortly afterwards I figured out how to find my old posts!

Should I cut off of the old flowerheads or is it too late now?