No, there is no problem in this case. It's very common for people to appear for interviews and obtain multiple offer letters during their notice period with the previous company. The tricky part is that your appointment letter is typically provided on the Date of Joining (DOJ) or a few weeks later. Mostly, it happens after you have joined the new company. Several factors are considered while issuing an appointment letter, such as compliance with HR policies, a cleared background check process, signed employment documents, statutory forms, etc. Usually, it happens on the day of your joining itself.
I am not sure how an appointment letter was sent to you before your Date of Joining (DOJ) - I mean, it generally doesn't happen in an ideal hiring scenario.