in the »Orkneyinger's Saga in chapter 59 they wrote about a historical figure: «Asleif was the name of his wife. She was wise, and of great family, and was much thought of for her own sake."
this historical sweyn asleif's son.
the website gaming geeks assigns the meaning of the name »asleif« with »god + Descendant«.
but the vikinganswerlady gives the most accurate explaination on the origin:
»Ásleif: god inheritance - For the prefix Ás- see below. For the suffix -leif see above. Appears in Orkneyingasaga (c. 1200) as the name of the wife of Ólafr Hrólfsson, the mother of Sveinn. This name also appears in Landnámabók for Ásleif Ţórgilsdóttir in ch. 94.«
the prefix and suffix:
»-as: Ása goddess A short form for names in Ás-, Ćs- or Ós-, which are from *ansuR and related to Old Icelandic áss or óss, «a god.» Found in the Anglo-Scandinavian form Asa. Occurs in Old Danish as Asa or Ose, and in Old Swedish Asa. Runic forms include nominative case aosa, asa, osa, the genitive case forms asu, osuahsu, asr, asu. (...)«
»-leif: The suffix -leif, -lćif or -löf is a feminine name element derived from Primitive Scandinavian *-laibó a formation from the stem in OW.Norse leif «inheritance, legacy», but as an element in personal names «one who comes after, heir» and thus to -lćifR/-lafR. Variants in -löf derive from a Primitive Scandinavian shortening of /ai/ > /a/.«
the website kabalarian philosophy writes about the meaning of the name the following, which i find surprisingly matching:
»Your first name of Asleif has given you a rather quiet, reserved, serious, studious nature. You have sensitivity and appreciation for the finer and deeper things of life, the beauties of nature, music, art, and literature. The people who mean the most to you are those who can offer you intellectual companionship. It is only when you are among those who understand your deeper nature that you can really be yourself. The experience of having your remarks taken lightly or belittled, particularly during the early years of your life, has caused you to keep your thoughts and feelings to yourself. You do not express yourself spontaneously when conversing with others; hence other people may often regard you as being aloof, and even unfriendly. Your difficulty in putting your deeper thoughts and feelings into words can lead to problems in more intimate associations. This name has caused you to live much within yourself. You are rather easily hurt or offended. At such times you can withdraw into a mood, and may not even speak to others. Aside from these points, this name contains many fine qualities. You are a thoughtful, analytical person, and you know your own mind, even though you may not speak it. You are very conscientious and competent in all that you do. You take seriously any responsibilities that you have--in the home, in the community, or at the job. Worry and mental depression could be problems in your life. Physically, any weaknesses in your health would centre in the heart, lungs, or bronchial organs.«