Algorithm for seasonal trends I have a very big table with lots of names and how much they are searched by date. 

I would like to find trending patterns. When does a name rise and when does it fall. Without knowing the name or the pattern before.
The rise could be during the seasons of the year but also during a week.

Like a 'warm hat' is trending in winter and falling in summer.
Or searches for a "board game" might rise on Sunday and decrease on Monday.

The table looks simplified like this:

winter gloves, 2014-01-01, 200
warm hat, 2014-01-01, 300
swimming short, 2014-01-01, 1
sunscreen, 2014-01-01, 2
....
winter gloves, 2014-07-01, 1
warm hat, 2014-07-01, 1
swimming short, 2014-07-01, 200
sunscreen, 2014-07-01, 300


Which algorithms should I have a look at? 

Thanks for any hint,
Joerg
As you are handling with time series data and you want to find trends; A good approach should be consider applying Holt-Winter's seasonal method. This algorithm handle seasonal, trend and smooth parameters. A good implementation of this kind of algorithm is Prophet by Facebook. You can code an exploratory analysis with this library and obtain trend, yearly seasonality, and weekly seasonality of the time series, among other components. Example: