Is there some logic in IC name prefixes?
Manufacturers often do use their own prefix for original products, or may continue to use a prefix of a company or product line that was acquired.

As the number of IC available has continuously grown the complexity of the naming schemes have become less obvious, and more exceptions exist. 

For example MAX- prefix typically refers to a Maxim IC, including the well-known MAX232 except MAX232 is also made by TI.

The NE5532 available from JRC, TI and On Semi, was originally designed by Signetics and continue to use the NE- prefix.

Other than business unit / company (original or acquired), the next most popular prefix convention would be series or technology based. Here I'm thinking of Op-Amps such as TL-, which are JFET or BiFET based op-amp technology AFAIK. 

Of course there are nearly as many exceptions to the rule as the rule covers, so like life, it's messy.