Is it necessary to use the same cable brand and model for bi-wiring??

You should select cables that compliment your speakers then biwire with identical cables

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By selecting cables, isn't that tone control?   You prefer tone the selected cable over others?  Every cable has a sonic characteristic?

Yes, all cables have a "character". 
What might be a wonderful and expensive cable might not be the best choice for certain speakers or amplifier. 
Find a good dealer who is familiar with your speakers and electronics and ask for their advice. 
Also, Music Direct sells a variety of cables at various price points and you can try them for a few weeks and have the option to return them if you aren't happy with the sound. 
Thats what dealers are for. 

Yes, all cables have a "character".

Right, you're tone controlling by selecting a cable.   So what's the difference in using same or different cables for bi-wiring, still tone control?

BTW, I would use the same cable for bi-wiring.

What might be a wonderful and expensive cable might not be the best choice for certain speakers or amplifier.
Find a good dealer who is familiar with your speakers and electronics and ask for their advice.
Also, Music Direct sells a variety of cables at various price points and you can try them for a few weeks and have the option to return them if you aren't happy with the sound.
Thats what dealers are for.

How's this relevant to the discussion on tone control?   

All of audio is about tone control. What difference does it make if I change speaker around to suit my cables, or change cables around to suit my speakers?
People basically change gear/cables around to suit their personal tastes. It's nothing to make a fuss about.

Put 10 audiophiles in a room to discuss biwire, and they will emerge with at least 11 different theories.

The majority of speakers today have biwire connections, however only a minority have been specifically designed for this from the ground up. For the rest it's just an add-on to maintain audio fashion. The manufacturers of the speakers that are specifically designed for biwire only recommend using two separate runs of identical cable for the biwire. So it appears they think it is necessary.

I agree that changing cables can make a difference in tonal character of the sound, however IMHO it doesn't make common sense to try and change high and low inputs on a speaker separately. That could cause an imbalance of frequencies at the crossover point.