Unfortunately there are no rigorous naming conventions for a gene. While some are based on actual molecular function or phenotypic effect, others can be totally bizarre names. Some are actually based on the test-tube and purification fraction labels. Some are named on characters from Mythology, novels etc.
I'll add some examples:
SNARE (proteins involved in vesicle fusion): Soluble NSF Activated protein REceptor (where NSF is N-maleimide sensitive factor).
Nanog: Inspired from an Irish folk tale. There is a magical land called Tír-na-nÓg where if one goes, becomes immortal and forever young. So the discoverers of this gene which responsible for stemness of a stem cell, named it as Nanog.
In fact, a lot of Drosophila genes are named after the visible phenotypic effect of the gene mutation. For e.g. Hairy, Wingless, Sex Combs Reduced etc.
Many genes were actually discovered before the genomes got fully sequenced and since these genes were well studied, the idea of renaming them would not have been very appealing. However, yeast genes have been given formal systematic names.
From SGD
YAL001C first ORF to the left of the centromere on chromosome I (A is the 1st letter of the English alphabet), on the complement or Crick strand
YGR116W 116th ORF right of the centromere on chromosome VII (G is the 7th letter of the English alphabet), on the Watson strand
While I agree that absence of any naming convention would not convey any information about the function of the gene, these wild names do make studying biology interesting. Yeast systematic genes names are so uninteresting and hard to remember (at least for me).
However, there are standard nucleotide repositories such as NCBI, ENA and DDBJ which maintain records about different genes. Moreover, there are standard organism specific databases such as FlyBase for Drosophila, TARE for Arabidopsis etc. In these databases you will find the standard names and description of these genes.
Also have a look at this post: Are there more descriptive ways of naming genes and gene interactions?Are there more descriptive ways of naming genes and gene interactions?