I'm skeptical; I mean, when you start a venture, you hope that it takes off. Will it still not be a problem if you gain 10, 30, 50 times the attention that you have now?
Good luck, though! Whatever bumps you hit, you will sort out along the way.
One good thing is that the name's phonology doesn't have the issue; just the spelling. Phonetically, it's just "packable".
I was not even aware "Paki" was a slur that refers to Pakistani individuals and never would have made the connection and I'm doubtful the average person would either. It's clearly a packaging company and so the mind makes that connection when reading the name.
in case you're curious:
The name we selected was "Packable" = packaging + enable/capable/etc.
But the domain was already taken. We searched for alterations of that until we landed on pakible.com being available.