Actually she'll probably be the only one around.
Jennifer is a pretty dated name no matter how you spell it. It's ugly so I get what you mean.
However I know a Jennyfer and she has it so much easier because her parents slightly altered it. Her last name is something super common (something like
Smith). Only because she spells it differently am I able to find her on the internet and I guess it helps with stuff like mail not being misdelivered (there must be several
Jennifer Smiths in our neighborhood but there's only one Jennyfer
Smith). So yeah I don't think it's entirely true that changing the spelling doesn't change anything, it can be helpful to have a different spelling of a common name.
There was a horror story about some guy who was denied credit because he had debts, supposedly. Turned out those weren't his debts but those of a guy with the exact same name (also something common) so I'd actually rather be Jennyfer
Smith or
Cateline Johnson than having his problems. This is only for when you have a super common surname, though.