never have problems with any registrar about that, but suppose there might be something in the TOS...
@atxsurf is correct - it is different for every registrar. However, their abillity and desire to enforce any such restrictions would likely be entirely based upon how you are using the mutliple accounts. Many people are resellers, web dev companies, etc., and may therefore manage multiple accounts on behalf of others so unless you are trying to engage in actions that harm the registrar (like cheating coupon restrictions), they probably won't care.
NO all domain reistars not permit more then 1 account with same name.So you may require to change other name
I don't know about the other registrars, but I wouldn't try any tricky stuff with Register.com in regards to coupons. They took 5 domains off me without warning because they felt I had misused they coupon policy. Apparently, I was not allowed to use the 4.95 coupon once I had already used the 2.95 coupon for new members. Apparently my account was locked into one type of coupon and i could only register using full pricing (35/year) henceforth. The customer service guy I talked to said their inbuilt system detected the "misuse" from my account and automatically dropped my domains from my account. I am not sure if their system would detect voucher exploitation from multiple accounts- perhaps it could, based on unique IP. But I certainly have learnt my lesson and wouldn't ever want to risk losing my domains again. I am not even sure I broke the rules, but then again the fine print might have something against voucher "misuse".
i dont like register.com, its for firs year very cheap. but for next year you wil charged 2x-10x. i hate this i ussualy use godaddy and namecheap