For those interested, here’s the reply I received from support:
[quote]I’m debating whether or not not to transfer a domain over to DreamHost
or let the old web hoster manage the domain name.
I’ve registered the name for a long time (5 years? 7 years?). If I
transfer that name to DreamHost will I still have that name registered
for that long period of a time or just for one year?
Your registration period will still stay the same but it will have an
DreamHost Support Team + firstname.lastname@example.org
Earn over $97 for each referral: http://www.dreamhost.com/rewards.html
To continue this support case, just reply to this email.
Open a new case at: https://panel.dreamhost.com/?tab=support