Sorry but I don't see any value.
How would this be used, and by who? In the UK hospitals use the NHS.UK TLD, like government use the .gov. USA hospitals seem to use .org, but maybe not all.
The "
X" can be replaced with 25 other characters or 10 numbers, in single digit, or a multitude of combos beyond a single digit, and "X" as a single digit isn't particularly amazing so not necessarily any better than double digits, such as XY or AA or 12 etc.
I only checked a few to hand reg and these are available for
$8:
hospital
b.com
hospital
c.com
hospital
w.com
Maybe "X" is better for some reason, but I cannot see why, sorry
Put it on some free marketplaces, Sedo etc, and perhaps you'll get a small return.
Hope that info helps you see the potential value in your name.
Good luck