No, there is no problem in this case.
Its very common - people do appear for interviews and obtain multiple offer letters during their notice period with the previous company.
Tricky part is - your appointment letter is typically provided on the DOJ or few weeks later. Mostly, it happens post your joining the new company. There are few factors that are considered while issuing an appointment letter - compliance with HR policies, cleared background check process, signed employment documents, statutory forms, etc. - typically it happens on the day of your joining itself.
I am not sure, how an appointment letter was floated to you before your DOJ even - I mean, it generally doesn't happen in an ideal hiring scenario.