Is this joke in bad taste?

Not such bad taste, but I liked it anyway:A man scanned the guests at a party and spotted an attractive woman standing alone. He approached her and asked her name.My name is Carmen," she told him."That's a beautiful name," he said. "Is it a family name?""No," she replied. "I gave it to myself. It reflects the things I
like most - cars and men."
"What's your name?" she asked."Beerfuck," he said.