Le Chat Noir probably has more to it than it's given credit for...

[h2mk]

I thought this was pretty interesting:

Looking through the wiki, one of the more interesting decorations in hamlet is the cat poster because of its relation to "Le Chat Noir"

Apparently, the place was closed after the guy who owned the place died but look at his name! According to Wikipedia his name was "Constant Maximin Rodolphe Salis on his birth certificate dated 30 May 1851". Oh, em, gee! Constant as in THE Constant? I don't know if it's a coincidence. The characters who seem most familiar with this are Warly, Wheeler, Wickerbottom and Maxwell. Wow! Four different characters recognizing it! Maxwell and Wheeler literally saying "Ah, the memories" and "I've been there" respectively. But Wagstaff just regards it as "Advertising.". And in case anyone else was curious, Warbucks says he's never heard of the place. Every other character says pretty much "Ooh it's a kitty!". I think this could possibly be where Klei got the name "Constant" from.

Here's one of the most interesting parts of the Wikipedia Article, regarding Don't Starve comparison:

"Writers who frequented the club wrote stories for the shadow theater that Rodolphe Salis, the owner of the cabaret, would read out loud after the performance. Thanks to the collaboration of many of the artists of that time, the stories were accompanied by some very complex colour, sound, and movement effects, making them more dynamic and exciting, as well as piano accompaniment."

Wheeler of course, has the voice of a piano, and this almost sounds like a description of a Maxwell show!

[Mantispidae]

DS has a tons of literary and historical references scattered around the place, its not any stretch to theorize more connections. 

However on the specific note of the name "The Constant" likely refers more directly to the state of the place more than anything- something unchanging and never ending, in the case of the survivors- an endless loop they will always return to regardless of death and a place who's greater power can not be unseated. It's this same meaning that the name Constant (Aswell as variants like Constantine) pull from; although it's carrying more of the positive spin of "Steadfast"