So many good choices! It’s going to be hard to decide. I like them all, but as of now I’m leaning towards Nathan, Ludwig, and Gateau.
I like Nathan. You are a baker, after all: and what goes perfectly with hot dogs? Fresh baked buns!
I always adopt older dogs. Sometimes house training is slower but it will happen. Just be patient. I grew up with a Dachs, They love to dig. They like tunnels and will be happy in they sleep in bed ,under the covers. They are warm for your feet. They are lap doggies and require a lot of petting. They absolutely love food .
Names" Subway, Torpedo, Hero.
Dusty Rose, I’m sorry to hear about the accident.
Baker, I recommend positive reinforcement training. With my semi-feral adoptee, my homemade solution was that when she peed in the house, I’d dip a paper towel in it, and take her and the towel outside and put the towel in the grass, make sure she sniffed it (no nose-rubbing or scolding), then praise her. Just to show her where that belonged, so to speak. And of course take her out early and often, every two hours at least. My rule for housetraining a puppy is, if, at any moment, you find that you’re comfortable, you should get up again and take the dog out.
In our case it worked well and fairly quickly, allowing for a few mistakes by both the dog and the humans. 
It was a tough decision but I’ve decided to go with “Nathan” as the name for my new doxie.
missred suggested it, along with a mustard yellow collar. Well I already have a yellow leash, so a collar will be easy.
Thanks to everyone for their ideas and names. They were all good, with something to recommend them. But Nathan really clicked.
I’ll see about getting pictures up somehow.
missred, where do I send the cookies?
Good choice! I can’t wait to see his pictures. I love weenie dogs.
Nathan’s a great name - congrats.
I’m going to put in a plug for Red Dingo. I’m not associated with them in any way, but I have a number of items from them for Tilly and Toby, and they’re great. Sturdy construction, sharp colors, very reasonable prices. A yellow collar with a red tag would be very hotdog dogish.
And I just noticed you have to go through a dog store to get their stuff. You can also get it on Amazon, or give them a call to find a local store.
In the old days, my mom trained dogs by yelling at them, sticking their nose in the pee and then pushing them out the back door.
Her dog Zelda looked out the back door and saw a squirrel. She peed on the floor next to us, stuck her nose in it and ran to the back door. She did not quite get it.
I’m so happy to see have adopted another dog and especially that you got one from a shelter. Nathan is a great name for a dachshund!
My shelter dog was already an adult when I got her and had never been housetrained (or trained at all really - we suspect she may have come from a puppymill sort of situation and never had a normal family before). It took some patience to get her to go outside consistently but she did catch on. She isn’t much of a barker so we trained her to ring a bell when she wants to go out: http://www.ehow.com/facts_4796617_potty-training-dogs-bell.html
I hope you have lots of fun with Nathan and that training him goes smoothly. 
Great name, missred! 
Yay for a new dog and good name! Good on you for giving him a good home, Baker!
Where are the pics of Nathan?! Don’t doggie threads have the same rules as kittie threads?! I demand pictures NOW! LOL
Seriously, Baker, congrats on the new weiner dog, Nathan’s a great (hot dog!) name.
I’ve pm’d you. I feel honored to have helped you name him. 
Perhaps, someday, I can meet the two of you at a dopefest.