Check the BSSID, that is, the access point's MAC address.
At home you'll usually have only one access point that's built into your router, so compare the MAC with the one written on the sticker on its bottom. (It might differ by a single digit in some cases.)
You didn't mention the OS you use, so I'll assume Linux:
$ iw wlan0 link
Connected to 24:a4:3c:ce:d2:16 (on wlan0)
SSID: eduroam
freq: 2462
...
Or you could check whether a scan detects multiple APs with the same name:
$ sudo iw wlan0 scan | egrep "^BSS|SSID"
$ nmcli -f in-use,ssid,chan,bars,security,bssid dev wifi list
There are various "Wi-Fi scanner" apps for Windows and macOS as well – can't recommend any, but most of them are able to display a basic "network list" including channels, BSSIDs, and all that. There's one from Nirsoft, and probably heaps of other freeware.
If you're on Windows (7 or later), the same can be done via netsh:
C:\> netsh wlan show interface
There is 1 interface on the system:
...
SSID : eduroam
BSSID : 24:a4:3c:ce:d2:16
Network type : Infrastructure
Radio type : 802.11n
...
(I can't remember offhand what's the command to request a scan, but it's also under netsh wlan show <something>.)
On macOS, this post suggests:
/System/Library/PrivateFrameworks/Apple80211.framework/Versions/A/Resources/airport -I en1
...
link auth: wpa2-psk
BSSID: 24:a4:3c:ce:d2:16
SSID: eduroam
MCS: -1 channel: 6
On FreeBSD, all that should be under ifconfig.
Android has quite a few "Wi-Fi analyzer" apps; at the time of posting, this one worked well.
The homepage, however, is not a network setting. Only your web browser cares about that.
Your homepage is configured on your client. If there are multiple SSIDs with the same name, and they are not protected, then there is no good way to differante them. If you had "reset" your router that means your wireless network wasn't protected with a password. – Ramhound – 2017-04-03T13:00:56.940
In what sense do you require a more precise way? – a CVn – 2017-04-03T13:02:42.590
Why is switching the router on/off non-technical? Because it's not fancy enough? – Kamil Maciorowski – 2017-04-03T13:02:51.983
If you only switched the router on/off it means all the settings is still the same – yass – 2017-04-03T13:15:30.550
@KamilMaciorowski: Because it causes unnecessary disruption (i.e. losing wireless and often wired connection) for what is a trivial status check. Not everyone lives alone. – user1686 – 2017-04-03T13:17:49.910
@grawity Unlike a factory reset...? – a CVn – 2017-04-03T13:30:57.543
@Ramhound, Router came with a 'reset to default' button, and I pressed it. Before that, I ensured my network was password protected, with SSID broadcast disable, and mac filtering enabled. and after I hit that button, everything was reset.(if it is my own network, that, I'm unsure of) – mathmaniage – 2017-04-03T14:51:30.180
@KamilMaciorowski, I was thinking of something unique to my router kind of identification – mathmaniage – 2017-04-03T14:52:49.050
Please edit the question so that "wifi" or "wireless" is in the title. Please include the OS(es) you use in the question. – Christopher Hostage – 2017-04-03T16:02:09.567
Are you trying to protect against something like an old access point that you might have configured with the same key and left plugged in? Or an innocent happenstance where someone chose the same SSID and key as you? Or are you trying to defend against a possibly hostile adversary? They're completely different problems. – David Schwartz – 2017-04-03T21:54:36.713
@DavidSchwartz , the second one, though I mentioned it in the question – mathmaniage – 2017-04-04T05:02:55.743
@ChristopherHostage , yes but there are answers for linux as well......... – mathmaniage – 2017-04-04T05:03:18.700