How to write your name in runes
There is no exact way, and the reason is honest: the Elder Futhark wrote sounds, not letters of your alphabet. A rune stands for a sound of a language spoken two thousand years ago, and your name carries sounds that row never wrote. You can come close, but every close version is a choice, not a translation.
Where this comes from
oldest description the oldest complete row: the Kylver stone · about AD 400
The row itself is attested: the Kylver stone in Gotland lists all twenty-four runes in order, carved around AD 400. What each letter wrote is read from inscriptions like it. That gives every rune a sound, but it gives your alphabet no map: some of your letters need two runes, some share one, and some sounds the carvers never wrote at all.
What the poems say
The poems are why the letters have names at all: feoh, ur, thorn. They say what each rune is, not how to spell with it. The row itself, sound by sound, is here.