I've never managed to do this effectively as I have with the Uniquiti / UniFi kit I bought.
(Made a wee thread at the time if you fancy some more reading:
https://forums.overclockers.co.uk/showthread.php?t=18726548)
While I've not had the need to have an extender until I moved home last year, in the past I've seen so many others try every solution under the sun to make this work and it always has its compromises.
The biggest problem you have that any consumer grade WiFi repeater operating on the same SSID is limited by the functionality of the WiFi controller on the device you're using (i.e. your phone or laptop)
The reason that most people choose to name their repeater with a separate SSID (and I stand by this decision myself with consumer grade stuff) is that your device is "sticky" and want to stay connected to something that "works". The biggest problem you've got that your devices are sticky as hell and when you name the SSID's the same you then can't choose which one to connect to.
So while you're looking for something that lets you give them the same SSID you end up with a crappy WiFi solution.
The UniFi kit resolves this by having built in controllers that allow the two access points to talk to one another and, in the background, move the sessions between the access points.
Other kit does this but keep in mind that 1) it's unlikely to exist on consumer products and 2) it's almost alway proprietary so you can't mix and match WiFi access points.
The same applies to the UniFi kit, it's proprietary stuff in the lower grade versions of their products (the sub £100 per access point range) but it is business class and works amazingly well.
Happy to recommend it to anyone that's facing the same problem and for my friend that's looking to move I'm suggesting he invests before even trying anything else.