Samuel (in Hebrew, Shmuel) does not mean “God has heard”: whoever told you that may be thinking it’s spelled שמוע-אל, i.e. “Shmua-el”, but it’s not. The consonant ayin is missing, and it doesn’t go missing lightly.
In the story of Samuel’s birth (I Sam. 1), Hannah, his mother, explains that she named him so—
כי מיהוה שאלתיו (ki meAdonai she’iltiv)
—i.e., ‘because from the Lord I have borrowed him’.
But that doesn’t make sense, because in that case, he should have been called Shaul (Saul)—which in fact was the name of the man whom Samuel (reluctantly) anointed as the first king of Israel many years later.
Rabbinical commentators, such as Rashi and Ibn Ezra, explained that this is because Shmu-el is a ‘fusion’ name, made of two words, sha’ul mi-El = ‘Borrowed from God’.
In answer to your second question, there is no name that means ‘servant heard’, but if you were to invent one, it might be:
עבד שמע Eved-Shamá (in anglicised form, perhaps Ebedsama), or:
ישמע עבד Yishmá-Eved (anglicised: Ismaebed).
(Originally written in reply to a question at Quora.com).
Notes by Autumn Light 