Is there a name for a total order in which every element has both a predecessor and a successor?
If $(T,\leq)$ is a total order and $x\in T$, then the successor of $x$ is the minimum of $\{y\in T:y>x\}$ and the predecessor is the maximum of $\{y\in T:y<x\}$, if they exist.
I know that these orders are all of the form $R\times\mathbb{Z}$ with the lexicographic ordering for some total order $R$; here I'm just looking for a nomenclature, if it exists.