“BBQ Hakadosh” makes no sense at all. The joke (highly inappropriate IMO) is in the play on Hakadosh Boruch Hu, and should not be done. Hashem’s name is not supposed to be taken in vain when we are making a BRACHA; kal v’chomer when it is for a joke.
The other names mentioned were slightly less offensive to me, but if they are offensive to others, they probably ought not be used. There is a fine line between making fun of someone and making a PUN out of someone’s name. In the case of Hashem, there is no question it should never be done.