Name of the highest power of 2 smaller than or equal to a given number

In the context of data structures - specifically, the van Emde Boas layout - I've heard this referred to as the hyperfloor of $x$. See “Cache-Oblivious B-Trees (Wayback Machine) by Bender, Demaine, and Farach-Colton for details - it defines the hyperfloor of $x$, denoted $\lfloor \lfloor x \rfloor \rfloor$, to be $2^{\lfloor \log_2 x \rfloor}$.

Hope this helps!

If $x$ is an integer, then $n+1$ is the bit length of $x$.

You could call it $2^{\lfloor \log_2(x) \rfloor}$.