If you're looking to install a different operating system on your phone, you really don't have many options. Manufacturers and carriers choose to lock the bootloader to prevent you from doing any modifications to your phone. A handful of phones do have this capability though.
Phones that can be unlocked by simply toggling the OEM Unlock option in Settings:
Essential PH-1 - an expensive phone that was designed to be open in the first place.
Google Pixel 2, 2XL, 3, 3XL, 4, 4XL - the ones that are factory unlocked only. If these phones were originally sold by Verizon or AT&T and later unlocked by an unlock code, would still have the bootloader locked.
Nokia 6 - international factory-unlocked version
OnePlus 5, 5T, 6, 6T, 7 Pro, 7T
And the following phones can have their bootloader unlocked by visiting the manufacturer's website and registering your serial number. The process is rather straightforward, but the manufacturer will know that the phone is unlocked, so any warranties will be voided, if you had any warranties to begin with.
- HTC U Ultra (carrier-unlocked model)
- HTC U11 (carrier-unlocked model)
- Huawei Honor 8
- Huawei Mate 9
- Huawei Mate 9 Pro
- Huawei P10
- Huawei P10 Plus
- LG V20 (US996 carrier-unlocked model)
- LG G6 (US997 carrier-unlocked model)
- Moto Z Force (2nd Generation)
- Moto Z Play (2nd Generation)
- Moto X4
- Moto G5
- Moto G5 Plus
- Sony Xperia XZ Premium (no OEM code required, but camera binaries wiped)
People unlock a bunch of other phones too. But that involves some degree of hacking. You would essentially be fighting the manufacturer and the carriers on this one. Sites like xda-developers.com are a good resource for such information. For you, as well, as the manufacturer, because once the manufacturer learns that a work-around has been achieved to unlock the bootloader on their phone or to root it, they would release a security update to patch the loophole.