Is your worktop laminate? Or stone?
I strongly recommend the sit-in sinks that are lowered from above into the hole in the worktop, and then retained with screws from underneath.
If you are keeping your old worktop, the new sink must cover the old hole, so measure it carefully and look for a new sink whose size and shape will do that. The hole can be enlarged or reshaped with a jigsaw. Most sinks are stainless steel and have a rectangular surround. Get one with a brushed finish, as mirror-finish shows scratches and scuffs.
If your laminate worktop is in a sensible colour such as white, you can buy a replacement that will match the rest of your kitchen. Plumbers are not expert carpenters but may be able to deal with a rectangular piece that doesn't need mitred corners, or to be fixed to another piece.
if you have a stone worktop you are doomed.
If you have a hardwood worktop it will be depressingly awkward.
If you are prosperous you can buy a sit-on sink that doesn't need a worktop, it fits onto a 1000mm kitchen unit. This is very good as drips, spills and splashes don't damage the worktop at the back of the sink.