I keep getting annoyed by Doodle. In this latest example, it proved impossible to change the shown "name" as guest user once my answer was submitted, despite it being possible to change everything else, or even decline. (I wanted to make use of the "name" field to include a single-word message to the organizer.) And when logged in the name field never even showed up during the answer flow.

Alternatives to Doodle

• https://crab.fit (it's FOSS, source code on Github)
• https://framadate.org/abc/en (FOSS, by the well-known French organization Framasoft)
• https://datumprikker.nl (not FOSS, but perhaps convenient since it offers Google and Apple apps). Don't forget to change to English in the menu.

Self-hostable alternatives

• https://github.com/lukevella/Rallly >2k stars, on v3.3.0, built on Next.js. Reddit thread.
• https://github.com/kellerben/dudle >300 stars, on v1.2, built on Ruby. Reddit thread.
• Nextcloud may have some doodle-like app (I haven't checked).