I've turned my ethernet-wired laptop into a hotspot using the hostednetwork with shared internet connection. When creating this hostednetwork, I used the same SSID as my router (linksys_xxx_xxxx), with the hopes of getting better WiFi on my android phone when I am near the laptop.
Will my phone have to reconnect if I move from one end of the house to the other? If I am standing in between the router and the laptop, will my phone realize that they are the same connections at either end, and choose the one with a better signal?
Yes, you're mostly right. Multiple routers with the same SSID will be considered as a part of the same network. This is analogous to Cell Towers. So when you move from one end to another, your phone will try to make a seamless transparent shift from one router to another of the same network. However your phone has no way of realising that they're the same connections on the other hand, but knowing that is mostly inconsequential.
The phone typically would not jump from one Access Point to another just because of a better signal reception. The jump typically happens if the signal strength is below a threshold and the device has detected another Access Point with the same SSID. (If you're programming the device, then you can make it do whatever you'd like anyways! :P)
It is also good to know that the device differentiates the APs based on BSSIDs (which are typically MAC addresses of the APs).