These variants can be synonyms, but whether they're interchangeable depends on usage. For example, the U.S. bureaucracy has several departments, all officially known as "Department of [noun]". All of these can be turned into interchangeable compound words for variety (e.g. Department of Justice = Justice Department, Department of Energy = Energy Department). Some compounds are more cumbersome and get used less often as a result, but they exist (Department of Housing and Urban Development = Housing and Urban Development Department).
Now, the same might be possible for your Center for Biomedical Ethics, but a big deciding factor would be usage. The convention with U.S. departments is well-established, but that's not necessarily so for other entities. If I wanted to make the Center for Biomedical Ethics into a compound, I would probably at least put it in lower case (biomedical ethics center) to show the reformulation is a one-off, not established practice.
As for your question on "love story" vs. "story of love", that gets into common nouns, and also is working in the opposite direction, which complicates things. As it happens, "love story" and "story of love" are synonyms, but they aren't fully interchangeable. The latter would be used if you wanted to modify "love" in some way (story of love everlasting) or list other things the story is about (story of love and adventure). But I'd say most common nouns that are compounds by default sound best that way. A form with "of" might sound more awkward, it might not exist, or it might have a different meaning.
For example, an "apple tree" is a tree that grows apples, while a "tree of apples" is either an awkward-sounding synonym or possibly the amount of apples you can get from a tree. For a subtler example, take "water bottle", which means a bottle intended to hold water, regardless of whether it currently contains water. Contrast that with "bottle of water", which is a bottle that currently contains water, regardless of whether it is intended to hold water.
N'hésite pas à corriger mes erreurs.