What are the rules for plasmid names?
So there are no rules per say (although I wish there were). But there are commonalities among plasmid names and they can help people identify them:

Include the empty backbone name in your plasmid name. This simple piece of information can often convey many important details. Once you know the backbone a plasmid is based on, you can usually derive: a) the bacterial antibiotic resistance, b) the promoter that drives the insert, and c) any other selection markers (for use in other cell types, e.g. eukaryotic cells).

Include information about the insert in your plasmid name. This is often a 3-6 letter representation of the gene (or DNA sequence).

Often researchers will add a lower case letter to the beginning of their insert abbreviation to specify what species it is. Example: ‘h’ is for Human (homo sapiens), ‘m’ is for mouse (mus musculus), ‘r’ is for rat (rattus rattus or rattus norvegicus), etc.

Add any tags or fusions that are on your insert. Typically you would list any tag or fusion protein in the order they appear in the plasmid and their relative position to the insert. Example, if you have a Flag tag on the N-terminal of your insert, you would list it first.

e.g.   pBACKBONE-Flag-hGene

If there was also an EGFP fused to the C-terminal of your insert you would list it after the insert.

pBACKBONE-Flag-hGene-EGFP

If your insert contains a mutation or modifcation, this should be included in the plasmid name.  Mutations are generally listed as the amino acid change and not a nucleotide change. The proper way to denote an amino acid mutation is to list the one letter abbreviation of the wild type amino acid immediately followed by its position (number) relative to the start Methionine (Met) followed by the one letter abbreviation of the mutated amino acid currently at that position.

Check for more information at Addgene.com they are the largest plasmid repository in the world.

By collisions I'm guessing you mean naming your plasmid something that is already "taken." This is a benefit of submitting to a repository, they will ensure this doesn't happen.if your planning on filing a patent, your parent attorney will do it.