There are a lot of words that end in h!:
with
filth
saith
youth
itch
pitch
ditch
wealth
And if names count,
Joseph
Josh
etc. etc!
Vanquish is an eight letter word. Vermouth is another word beginning with v and ending with h.
Some five letter words ending in H are:batchbeachbelchbirchbirthblushbrashbrushbunchcatchcoachconchcouchcrashcrushdeathearthfetchfifthflashfleshflushforthfreshgnashhatchlatchlunchlurchmarshmatchmorphneathninthnorthpeachperchplushpoochporchreachsixthslushsoothsouthteachtenthtoothtruthyouth
Who are you with
hash
Slashsmashgnashbrashcrashstash.
Hanukkah
astonish
bath
hurrah, huzzah
Hearth.
One is through.
scottish