Whether you want to memorise the names or not, it's a matter of choice, time, effort you are willing to dedicate.
However we should comply with the the standards and recommendations on taxonomy, which in my view does share qualities with any ontology (i.e. hierarchy, standards).
How to write scientific names for animals?
Latin names for species should be in italics.
The genus component of the name should be in upper case e.g. Felis catus is OK, felis catus is not OK.
The species component of the name should be in lower case e.g. Mus musculus is OK, Mus Musculus is not OK.
Depending on the context, these rules could (would) be lifted. In you do code for example, you will not write those in italics.
I don't think there is such a thing as redundant information. The more you work with felic catus the more you will now it is Felis catus. The more you will know it equals
cat.
It's important to get the name right. It's UniProt, not Uniprot or uniprot.
It may sound pedantic. It may be pendantic. But we need to use the right name. The wrong piece of code may make a difference, give you an error or give you wrong output. So details are important.
I look at information as relevant information. Some is very relevant information, others not so much so.
Note, we say mm10 for the genome assembly for mouse, because mm = Mus musculus.
If I am understanding you correctly, you are asking if you need to learn the genus/species of every plant and animal? Good luck with that. Those just fall under:
Kingdom->Phylum->Class->Order->Family->Genus->Species
This is how different organisms are grouped in science and it is called taxonomy. When referring to a specific organism (such as the ones listed above) usually just the genus/species is given as the identifier. If you are working with a particular organism, or group of organisms of interest (such as bacteria or cats or whatever) it may be useful for you to know which genus/species you are working with. This may be particularly useful if you are using a prebuilt reference genome for a specific bacteria or plant, but other than that I don't know where you would use genus/species in analysis.
From a practical point of view, scientific names are the only sure way of unambiguously identifying an organism because vernacular names are too variable. Native speakers of a given language do not necessarily agree on a common name for a given organism.
If you're not a native speaker of English, you'll have to learn the English names for species you work with anyway. For example, as a French speaker, I knew what a danio (name of the zebrafish in French) was but not what a zebrafish was until I saw the scientific name of the zebrafish.
They should know these on a 'need to know' basis.
Since this is more asking for an opinion than a question which has a definite answer I have converted this to a "Forum" post.