Is prince's love symbol a Unicode character?

Answer 1

No it is not. According to the Unicode manual:

Note, however, that the Unicode Standard does not encode idiosyncratic, personal, novel, or private-use characters, nor does it encode logos or graphics.

Accordingly, an enormous amount of pressure by outside bodies would be necessary to have Unicode include invented characters only as a substitute for one person's single name.

To include any symbol invented by any person as their name symbol would be absurd. One might restrict the added symbols only to those invented by so-called "important people", but that is rather snobbish. How does one establish the exact point at which a person becomes important enough?

If publishers began to use the Prince love symbol, encoded as a private-use character, often, then it would be encoded as it would be needed for interchanging texts. The same would be true for a non-standard mathematical symbol.

As of now, the Prince love symbol is simply one example of an "idiosyncratic, personal, novel" symbol.