I don't think it's egocentric to include your name in the combo. And personally, I much prefer
Annelise to most other forms of
Anne, I think it is a very pretty name.
Some suggestions:
Annelise JuneAnnelise Nanette (probably a bit much, but just wanted to sneak it in, lol)
Annelise RubyAnnelise RoseAnnelise JadeAnnelise VivianAnnelise IvyAnnelise KatherineAnnelise FaithAnnelise CaseyAnnelise ClaireAnnelise RhiannonAnnelise NeveAnnelise PhoebeAnnelise PhaedraAnnelise MaeveAnnelise Frances
Like any?