There will be hundreds of different brackets out there, so the chances of finding the same bracket are fairly slim. You might hit lucky and find they bought a popular one from Currys, or they could have just as easily ordered a cheap, unbranded bracket from Amazon (or elsewhere), in which case tracking it down will be much harder. The more popular manufacturers often put specifications on their websites though so if you do find a visual match, you may be able to check the measurements of the markings on your wall with their diagrams.
One thing to consider is even if you did manage to track it down, there's no guarantee it'll be suitable for your TV (VESA spacing, weight) and if you're planning on getting a new TV, I personally wouldn't want my choice restricted to one that will fit.
TBH though, I'm not sure if I would trust someone else's DIY to support my TV and would want to fit my own anyway. If it's a stud/plasterboard wall then, provided your plasterboard is sound, there should be no issues with drilling further holes, provided they don't get too close to the existing holes. Buying a bracket with plenty of options for mounting holes and further options for varying the height of the TV on the bracket should help you to locate it in a new position, clear of the existing holes. Ideally, at least some of the holes would be into the stud woodwork but that isn't always an easy thing to achieve. If it's a brick wall, then drilling new holes nearby will be even less of an issue.
If the existing bolts do seem secure and you can't find an exact match, then one option would be to buy a bracket with a larger vertical distance between the two rows of mounting holes, such as one with a design like
this. That would allow you to use the existing top bolts and should ensure that the new row of bottom holes are far enough away from the existing lower holes so as not to cause any issues with the plasterboard's integrity.
If you do drill any new holes, then you'll have to take care as it's likely there will be mains and other A/V cables behind, judging by your photo.