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I'm reading a manga and I've seen "nameや" a couple times now, but I'm not sure what it means exactly. Does it show affection?

Two examples:

There are two types of や which should be distinguished.

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  や as 終助詞 (sentence-ending particle) or 間投助詞 (interjectory particle): A casual vocative particle. In English, "hey" as in "Hey Siri" or "o" as in "O Lord" is similar in purpose. But this type of や sounds old-fashioned and is found almost exclusively in fiction, fairly tales, etc. It can follow an arbitrary person name, and ～や is not grammatically related to the following part of the sentence.
  
  

  
  

  ≪終助≫ 目下の相手に対する呼びかけを表す。「太郎や、帰ったのかい」「ポチや、こっちにおいで」 _{[明鏡国語辞典 第二版]}

  
  
  

  ≪間助≫ 名詞、名詞に準じる語、副詞に付く。呼びかけを表す。「花子や、ちょっとおいで」_{[デジタル大辞泉]}

  
  

  
  


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  や as 接尾語 (suffix): A suffix is a component to form another word. An English equivalent of this type of や is "-ie" as in "doggie" or "Kathie". The resulting word is another noun, so you can say 坊やが寝ている, じいやを呼べ, etc. You cannot attach it to an arbitrary name. Actually, this や is found in a very limited set of nouns, and IMHO ぼうや, じいや and such should be learned as distinct nouns.

  
  
  

  
  

  ≪接尾≫《人を表す名詞に付いて》親しみの意を表す。「坊や・ねえや・ばあや・じいや」 _{[明鏡国語辞典 第二版]}

  
  
  

  ≪接尾≫ 人を表す名詞や人名などに付いて、親しみの意を添える。「ねえや」「坊や」「爺や」「きよや」_{[デジタル大辞泉]}

  
  

  
  

Since メアリ is a Western person name, this や in メアリや is not a suffix but the vocative-や. メアリや means "Oh Mary", "Listen, Mary" or simply "Mary!" You can not say something like メアリやが女王になる. The vocative-や is sometimes used even after a name suffix, (e.g., お前さんや "(Hey) You!") or a suffix-や (e.g., ばあやや, "(Hey) Grandma!")

You are right, it shows affection.

According to the dictionary, や is a suffix for names or nouns to show affection.

や: ［接尾］人を表す名詞や人名などに付いて、親しみの意を添える。「ねえや」「坊や」「爺や」「きよや」
https://dictionary.goo.ne.jp/jn/220995/meaning/m0u/や/