It can indeed be jarring, and one of my pet hates is when a character's full name is given in the first sentence. It doesn't have to be jarring, and, often, using a single name rather than the firstname-surname combination comes across more smoothly, especially if it's done without a descriptor (so 'Jane' rather than 'Jane Doe' or 'red-haired teacher Jane Doe').
How I do it depends what I'm writing. For one of my current WIPs it's very easy. It's in omniscient so I just name each character as he/she/it/they appears in the text.
For my other it's much harder. That one is in very close third (think Wolf Hall-close) and we're in the protagonist's head all the time. He is only ever named in dialogue; he's not as self-confident as Cromwell in Bring Up the Bodies and so doesn't think of himself as "he, Sigmund*". This means I have to be careful - very careful - with pronouns and antecedents, especially when Sigmund's interacting with another man or men. Other characters are named of course, if Sigmund knows their names. If he doesn't they get called things like the 'hedge-witch' or 'the South Point man'. Beta readers haven't complained so far, but I know it's one of those choices that some people will dislike. I can live with that, because I think it works for the character and the story.
In first person (I don't write first person) I think I'd do what MadAlice suggests and have someone use the name first. Or have someone ask directly for the name. That's what I did with my close third WIP. (Looking at that, Sigmund gives his name as word 424 in response to somebody asking for it: it happens smoothly enough, I think.)
* not his actual name