ASV's ID's question

I have a general question about ASV's.
I read the article and it was not clear to me how ASV's ID's are assigned! I mean, is this random ?
My question comes from the idea that I have my data in different libraries and I run DADA2 for each one. So, at the end I merged the tables and sequences that came from each run/library. So, If the ASV's ID's are different assigned for each taxon I don't know if this issue could affect beta diversity calculations.
If so, do I have to clustered my ASV's into OTU's with the cluster de novo approach? or maybe to cluster into a level like genus ? The effect of batch in this case may be a problem for me with the diversity calculations?

I believe this topic is highly relevant to your questions, so you can read excellent explanation provided there. Please, feel free to ask here additional questions if they are not covered by the link.

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Thanks for your answer!