It’s not your fault.
A lot of people forget someone’s name when they are introduced for the first time. Then it’s embarrassing having to ask again.
The reason why we struggle to remember is because our memories fall into two buckets, long term memory and short term memory.
Remembering names means using your short term memory which only holds a little bit of information and you are already focusing on what you are going to say or how you will move to process the information of the introduction.
We might think we are good at multi taskers but generally we are not especially when trying to take in new information simultaneously as giving out information.
A good way to remember someone’s name is to repeat their name when they are introduced to you, saying nice to meet you followed by their name or something similar.
The repetition helps the name stick.