As far as i know (i checked my visa too), Annotation is for dependants.
only the PA, principal applicant name
H4 Visa should have the H1’s name under Annotation.
But still, your H1 visa should have info like,
PN (Petitioner) : Company Name
PN# : EAC or WAC (receipt number)
PED: Petition Expiration Date
You must send an email to the consular post where you applied asking this concern with the Visa number (the one in red to the right side bottom of visa). Its better to scan a copy of the visa and send it in the email, I believe it might cause issues in PoE, so why to take a risk