The Sony VAIO VPCEB34EN uses an i3-370M CPU.
According to Intel specification, this i3-370M CPU supports up to 4 GB modules. There is no support for 8 GB modules.
If wanting 8 GB total memory for the VAIO VPCEB34EN, then two 4 GB modules will have to be used. A single 8 GB module can not be used. So, to use 8 GB total system memory, two 4 GB modules will have to be used. There is no other option.
Basically, each slot supports up to 4 GB only. The slots do not support 8 GB memory.
As stated previously, an 8 GB kit consisting of 2 x 4 GB modules is the preferred option, as the modules are guaranteed to be compatible with each other. But as also mentioned previously, the only known compatible 8 GB kit (with 2 x 4 GB modules) is the Crucial kit CT2KIT51264BF160B. However, this kit doesn't appear to be available from your four stores listed above.
And again as previously mentioned, the next best option is to use two single/individual modules (two 1 x 4 GB) which are not from a kit. As the modules are not from a kit, there is a possibility the modules may not work together properly due to memory module characteristic variations. But there is a chance the modules may work together, if lucky.
The suggested 4 GB modules are Crucial part number CT51264BF160B. These modules run at 1.35 V.
1.35 V modules will be run at 1.50 V when used together with 1.50 V modules. The 1.35 V modules can run at 1.50 V with no problem.