Blue's Untaken Names List
All names swiped from Zoombinis.

If none of those names work for you, try /~Bublin

Blue's list of probably-stuck semi-BD pets

Dumbinho31 the Brown Kyrii
http://www.neopets.com/petlookup.phtml?pet=Dumbinho31
Level: 3
Hit Points: 33 / 23
Strength: GREAT (22)
Defence: godly
Movement: breakneck
Intelligence: master genius (62)

midnight2789 the Blue Pteri
http://www.neopets.com/petlookup.phtml?pet=midnight2789
Level: 3
Hit Points: 57 / 51
Strength: GREAT (25)
Defence: heavy
Movement: GREAT (29)
Intelligence: mega genius (52)

mrota the Blue Techo
http://www.neopets.com/petlookup.phtml?pet=mrota
Level: 1
Hit Points: 63 / 33
Strength: GREAT (25)
Defence: below average
Movement: mach 2
Intelligence: genius

Ruby_x24 the White Tuskaninny
http://www.neopets.com/petlookup.phtml?pet=Ruby_x24
Level: 4
Hit Points: 22 / 22
Strength: GREAT (25)
Defence: below average
Movement: fast
Intelligence: super genius (46)

Shorteen the Yellow Mynci
http://www.neopets.com/petlookup.phtml?pet=Shorteen
Level: 5
Hit Points: 0 / 42
Strength: GREAT (24)
Defence: heavy
Movement: speedy
Intelligence: average

goodemily the Electric Moehog
http://www.neopets.com/petlookup.phtml?pet=goodemily
Level: 2
Hit Points: 19 / 19
Strength: GREAT (22)
Defence: tough
Movement: fast
Intelligence: average

Let_It_Be_4Ever the Snow Flotsam
http://www.neopets.com/petlookup.phtml?pet=Let_It_Be_4Ever
Level: 2
Hit Points: 18 / 21
Strength: GREAT (21)
Defence: armoured
Movement: speedy
Intelligence: average

Storm_102 the Blue Koi
http://www.neopets.com/petlookup.phtml?pet=Storm_102
Level: 26
Hit Points: 65 / 22
Strength: GREAT (32)
Defence: GREAT (28)
Movement: GREAT (22)
Intelligence: ULTIMATE GENIUS (128)

keykey6201945 the Green Xweetok
http://www.neopets.com/petlookup.phtml?pet=keykey6201945
Level: 30
Hit Points: 9 / 9
Strength: GREAT (39)
Defence: GREAT (32)
Movement: GREAT (30)
Intelligence: master genius (65)

I found these through a search engine, with the following search terms:

Note that you will find pets owned by people who have their name as "in the pound".
Simply add their usernames to the end, with a dash (-) in front, and those results will be filtered out.
Others will have found an owner since the last time the search engine saw their page, so don't get too attached to names/colours.